From: couchot Date: Tue, 15 Jul 2014 19:14:20 +0000 (+0200) Subject: ajout des fichiers initiaux X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/14Secrypt.git/commitdiff_plain/9d0171e68668964f8cac0a2c4e83553c825def49 ajout des fichiers initiaux --- 9d0171e68668964f8cac0a2c4e83553c825def49 diff --git a/Example.tex b/Example.tex new file mode 100644 index 0000000..fac226f --- /dev/null +++ b/Example.tex @@ -0,0 +1,362 @@ +\documentclass[a4paper,twoside]{article} + +\usepackage{epsfig} +\usepackage{subfigure} +\usepackage{calc} +\usepackage{amssymb} +\usepackage{amstext} +\usepackage{amsmath} +\usepackage{amsthm} +\usepackage{multicol} +\usepackage{pslatex} +\usepackage{apalike} +\usepackage{SCITEPRESS} +\usepackage[small]{caption} + +\subfigtopskip=0pt +\subfigcapskip=0pt +\subfigbottomskip=0pt + +\begin{document} + +\title{Authors' Instructions \subtitle{Preparation of Camera-Ready Contributions to SCITEPRESS Proceedings} } + +\author{\authorname{First Author Name\sup{1}, Second Author Name\sup{1} and Third Author Name\sup{2}} +\affiliation{\sup{1}Institute of Problem Solving, XYZ University, My Street, MyTown, MyCountry} +\affiliation{\sup{2}Department of Computing, Main University, MySecondTown, MyCountry} +\email{\{f\_author, s\_author\}@ips.xyz.edu, t\_author@dc.mu.edu} +} + +\keywords{The paper must have at least one keyword. The text must be set to 9-point font size and without the use of bold or italic font style. For more than one keyword, please use a comma as a separator. Keywords must be titlecased.} + +\abstract{The abstract should summarize the contents of the paper and should contain at least 70 and at most 200 words. The text must be set to 9-point font size.} + +\onecolumn \maketitle \normalsize \vfill + +\section{\uppercase{Introduction}} +\label{sec:introduction} + +\noindent Your paper will be part of the conference proceedings +therefore we ask that authors follow the guidelines explained in +this example in order to achieve the highest quality possible +\cite{Smith98}. + +Be advised that papers in a technically unsuitable form will be +returned for retyping. After returned the manuscript must be +appropriately modified. + +\section{\uppercase{Manuscript Preparation}} + +\noindent We strongly encourage authors to use this document for the +preparation of the camera-ready. Please follow the instructions +closely in order to make the volume look as uniform as possible +\cite{Moore99}. + +Please remember that all the papers must be in English and without +orthographic errors. + +Do not add any text to the headers (do not set running heads) and +footers, not even page numbers, because text will be added +electronically. + +For a best viewing experience the used font must be Times New +Roman, except on special occasions, such as program code +\ref{subsubsec:program_code}. + + +\subsection{Manuscript Setup} + +\noindent The template is composed by a set of 7 files, in the +following 2 groups:\\ +\noindent {\bf Group 1.} To format your paper you will need to copy +into your working directory, but NOT edit, the following 4 files: +\begin{verbatim} + - apalike.bst + - apalike.sty + - article.cls + - scitepress.sty +\end{verbatim} + +\noindent {\bf Group 2.} Additionally, you may wish to copy and edit +the following 3 example files: +\begin{verbatim} + - example.bib + - example.tex + - scitepress.eps +\end{verbatim} + + +\subsection{Page Setup} + +The paper size must be set to A4 (210x297 mm). The document +margins must be the following: + +\begin{itemize} + \item Top: 3,3 cm; + \item Bottom: 4,2 cm; + \item Left: 2,6 cm; + \item Right: 2,6 cm. +\end{itemize} + +It is advisable to keep all the given values because any text or +material outside the aforementioned margins will not be printed. + +\subsection{First Section} + +This section must be in one column. + +\vfill +\subsubsection{Title and Subtitle} + +Use the command \textit{$\backslash$title} and follow the given structure in "example.tex". The title and subtitle must be with initial letters +capitalized (titlecased). If no subtitle is required, please remove the corresponding \textit{$\backslash$subtitle} command. In the title or subtitle, words like "is", "or", "then", etc. should not be capitalized unless they are the first word of the subtitle. No formulas or special characters of any form or language are allowed in the title or subtitle. + +\subsubsection{Authors and Affiliations} + +Use the command \textit{$\backslash$author} and follow the given structure in "example.tex". + +\subsubsection{Keywords} + +Use the command \textit{$\backslash$keywords} and follow the given structure in "example.tex". Each paper must have at least one keyword. If more than one is specified, please use a comma as a separator. The sentence must end with a period. + +\subsubsection{Abstract} + +Use the command \textit{$\backslash$abstract} and follow the given structure in "example.tex". +Each paper must have an abstract up to 200 words. The sentence +must end with a period. + +\subsection{Second Section} + +Files "example.tex" and "example.bib" show how to create a paper +with a corresponding list of references. + +This section must be in two columns. + +Each column must be 7,5-centimeter wide with a column spacing +of 0,8-centimeter. + +The section text must be set to 10-point. + +Section, subsection and sub-subsection first paragraph should not +have the first line indent. + +To remove the paragraph indentation (only necessary for the +sections), use the command \textit{$\backslash$noindent} before the +paragraph first word. + +If you use other style files (.sty) you MUST include them in the +final manuscript zip file. + +\subsubsection{Section Titles} + +The heading of a section title should be in all-capitals. + +Example: \textit{$\backslash$section\{FIRST TITLE\}} + +\vfill +\subsubsection{Subsection Titles} + +The heading of a subsection title must be with initial letters +capitalized (titlecased). + +Words like "is", "or", "then", etc. should not be capitalized unless +they are the first word of the subsection title. + +Example: \textit{$\backslash$subsection\{First Subtitle\}} + +\subsubsection{Sub-Subsection Titles} + +The heading of a sub subsection title should be with initial letters +capitalized (titlecased). + +Words like "is", "or", "then", etc should not be capitalized unless +they are the first word of the sub subsection title. + +Example: \textit{$\backslash$subsubsection\{First Subsubtitle\}} + +\subsubsection{Tables} + +Tables must appear inside the designated margins or they may span +the two columns. + +Tables in two columns must be positioned at the top or bottom of the +page within the given margins. To span a table in two columns please add an asterisk (*) to the table \textit{begin} and \textit{end} command. + +Example: \textit{$\backslash$begin\{table*\}} + +\hspace*{1.5cm}\textit{$\backslash$end\{table*\}}\\ + +Tables should be centered and should always have a caption +positioned above it. The font size to use is 9-point. No bold or +italic font style should be used. + +The final sentence of a caption should end with a period. + +\begin{table}[h] +\caption{This caption has one line so it is +centered.}\label{tab:example1} \centering +\begin{tabular}{|c|c|} + \hline + Example column 1 & Example column 2 \\ + \hline + Example text 1 & Example text 2 \\ + \hline +\end{tabular} +\end{table} + +\begin{table}[h] +\caption{This caption has more than one line so it has to be +justified.}\label{tab:example2} \centering +\begin{tabular}{|c|c|} + \hline + Example column 1 & Example column 2 \\ + \hline + Example text 1 & Example text 2 \\ + \hline +\end{tabular} +\end{table} + +Please note that the word "Table" is spelled out. + + +\subsubsection{Figures} + +Please produce your figures electronically, and integrate them into +your document and zip file. + +Check that in line drawings, lines are not interrupted and have a +constant width. Grids and details within the figures must be clearly +readable and may not be written one on top of the other. + +Figure resolution should be at least 300 dpi. + +Figures must appear inside the designated margins or they may span +the two columns. + +Figures in two columns must be positioned at the top or bottom of +the page within the given margins. To span a figure in two columns please add an asterisk (*) to the figure \textit{begin} and \textit{end} command. + +Example: \textit{$\backslash$begin\{figure*\}} + +\hspace*{1.5cm}\textit{$\backslash$end\{figure*\}} + +Figures should be centered and should always have a caption +positioned under it. The font size to use is 9-point. No bold or +italic font style should be used. + +\begin{figure}[!h] + %\vspace{-0.2cm} + \centering + {\epsfig{file = SCITEPRESS.eps, width = 5.5cm}} + \caption{This caption has one line so it is centered.} + \label{fig:example1} + \end{figure} + +\begin{figure}[!h] + \vspace{-0.2cm} + \centering + {\epsfig{file = SCITEPRESS.eps, width = 5.5cm}} + \caption{This caption has more than one line so it has to be justified.} + \label{fig:example2} + \vspace{-0.1cm} +\end{figure} + +The final sentence of a caption should end with a period. + + + +Please note that the word "Figure" is spelled out. + +\subsubsection{Equations} + +Equations should be placed on a separate line, numbered and +centered.\\The numbers accorded to equations should appear in +consecutive order inside each section or within the contribution, +with the number enclosed in brackets and justified to the right, +starting with the number 1. + +Example: + +\begin{equation}\label{eq1} + a=b+c +\end{equation} + +\subsubsection{Program Code}\label{subsubsec:program_code} + +Program listing or program commands in text should be set in +typewriter form such as Courier New. + +Example of a Computer Program in Pascal: + +\begin{small} +\begin{verbatim} + Begin + Writeln('Hello World!!'); + End. +\end{verbatim} +\end{small} + + +The text must be aligned to the left and in 9-point type. + +\vfill +\subsubsection{Reference Text and Citations} + +References and citations should follow the Harvard (Author, date) +System Convention (see the References section in the compiled +manuscript). As example you may consider the citation +\cite{Smith98}. Besides that, all references should be cited in the +text. No numbers with or without brackets should be used to list the +references. + +References should be set to 9-point. Citations should be 10-point +font size. + +You may check the structure of "example.bib" before constructing the +references. + +For more instructions about the references and citations usage +please see the appropriate link at the conference website. + +\section{\uppercase{Copyright Form}} + +\noindent For the mutual benefit and protection of Authors and +Publishers, it is necessary that Authors provide formal written +Consent to Publish and Transfer of Copyright before publication of +the Book. The signed Consent ensures that the publisher has the +Author's authorization to publish the Contribution. + +The copyright form is located on the authors' reserved area. + +The printed form should be completed and signed by one author on +behalf of all the other authors, and uploaded through the authors' reserved area. Alternatively, you can send it to the secretariat by e-mail or fax. + +\section{\uppercase{Conclusions}} +\label{sec:conclusion} + +\noindent Please note that ONLY the files required to compile your paper should be submitted. Previous versions or examples MUST be removed from the compilation directory before submission. + +We hope you find the information in this template useful in the preparation of your submission. + +\section*{\uppercase{Acknowledgements}} + +\noindent If any, should be placed before the references section +without numbering. To do so please use the following command: +\textit{$\backslash$section*\{ACKNOWLEDGEMENTS\}} + + +\vfill +\bibliographystyle{apalike} +{\small +\bibliography{example}} + + +\section*{\uppercase{Appendix}} + +\noindent If any, the appendix should appear directly after the +references without numbering, and not on a new page. To do so please use the following command: +\textit{$\backslash$section*\{APPENDIX\}} + +\vfill +\end{document} + diff --git a/SCITEPRESS.eps b/SCITEPRESS.eps new file mode 100644 index 0000000..45e720a Binary files /dev/null and b/SCITEPRESS.eps differ diff --git a/SCITEPRESS.sty b/SCITEPRESS.sty new file mode 100644 index 0000000..8b5b5be --- /dev/null +++ b/SCITEPRESS.sty @@ -0,0 +1,162 @@ +\typeout{Conference Style for SCITEPRESS for LaTeX 2e -- version of April 2013} + +\pagestyle{empty} +\setlength\paperheight{297mm} +\setlength\paperwidth{210mm} + + +\setlength\topmargin{-0.91in} \setlength\oddsidemargin{0.02362in} +\setlength\evensidemargin{0.02362in} + +\setlength\textheight{8.74in} \setlength\textwidth{6.221in} +\setlength\columnsep{0.8cm} +\newlength\titlebox %\setlength\titlebox{2in} +\setlength\headheight{0pt} \setlength\headsep{36pt} +\thispagestyle{empty} \pagestyle{empty} + +\flushbottom \twocolumn \sloppy + +\def\addcontentsline#1#2#3{} + + + +%%First Section +\def\title#1{\gdef\@title{ #1 \\[15pt]{\textmd {\textbf }}\\}} +\newcommand{\subtitle}[1]{\\ \fontsize{13}{15}\selectfont \textit{#1 } } + +\def\keywords#1{\gdef\@keywords{\small Keywords: \hspace{0.388cm} \begin{minipage}[t]{5.45in} \fontsize{9}{11}\selectfont \vspace{-0.22cm} #1 \\ \end{minipage}}} +%\gdef\@mykeywords{} +\def\abstract#1{\gdef\@abstract{\ \\ \small Abstract: \hspace{0.6cm} \begin{minipage}[t]{5.45in} \fontsize{9}{11}\selectfont \vspace{-0.22cm} #1 \end{minipage} }} + +%%%%%%% +\def\sup#1{$^{#1}$} + +\newcommand{\authorname}[1]{\fontsize{11}{13}\selectfont #1 \\ }%\addtocounter{authorcounter}{1}} +\newcommand{\affiliation}[1]{\begin{minipage}[t]{6.2in} \centering \fontsize{9}{11}\selectfont \textit{ #1} \end{minipage} \\} +\newcommand{\email}[1]{\fontsize{9}{11}\selectfont \textit{#1} \\[12pt]} + + +%%%%%%% +\def\maketitle{\par +\begingroup +% to make the footnote style local to the title +\def\thefootnote{\fnsymbol{footnote}} +\twocolumn[ + +\centering {\LARGE\bf \@title \par} +\vskip -0.07in + +\centering\@author +\vskip 0.51in + +\@keywords +\vskip 0.02in + +\@abstract + +\vspace{32pt} + +] + + +\@thanks +\endgroup + +\let\maketitle\relax \let\@maketitle\relax +\gdef\@thanks{}\gdef\@author{}\gdef\@title{}\let\thanks\relax} + + + +%%Paper Contents and References + +\def\pubnote#1{\thispagestyle{myheadings} +\pagestyle{myheadings} +\markboth{#1}{#1} +\setlength\headheight{10pt} \setlength\headsep{10pt} +} + +% sections with less space +\def\section{\@startsection{section}{1}{\z@}{24pt plus 2pt minus 1pt} +{12pt plus 2pt minus 1pt}{\Large\bf\raggedright}} +\def\subsection{\@startsection{subsection}{2}{\z@}{-2.0ex plus +-0.5ex minus -.2ex}{12pt plus 2pt minus 1pt}{\large\bf\raggedright}} +\def\subsubsection{\@startsection{subsubsection}{3}{\z@}{-2.0ex plus +-0.5ex minus -.2ex}{12pt plus 2pt minus 1pt}{\normalsize\bf\raggedright}} + + +% Footnotes +\footnotesep 6.65pt % +\skip\footins 9pt plus 4pt minus 2pt +\def\footnoterule{\kern-3pt \hrule width 5pc \kern 2.6pt } + +% Lists and paragraphs +\parindent 0.5cm +\topsep 4pt plus 1pt minus 2pt +\partopsep 1pt plus 0.5pt minus 0.5pt +\itemsep 2pt plus 1pt minus 0.5pt +\parsep 2pt plus 1pt minus 0.5pt +\leftmargin 15pt \leftmargini\leftmargin \leftmarginii 10pt +\leftmarginiii 5pt \leftmarginiv 5pt \leftmarginv 5pt \leftmarginvi +5pt \labelwidth\leftmargini\advance\labelwidth-\labelsep \labelsep +5pt +\def\@listi{\leftmargin\leftmargini} +\def\@listii{\leftmargin\leftmarginii +\labelwidth\leftmarginii\advance\labelwidth-\labelsep +\topsep 2pt plus 1pt minus 0.5pt +\parsep 1pt plus 0.5pt minus 0.5pt +\itemsep \parsep} +\def\@listiii{\leftmargin\leftmarginiii +\labelwidth\leftmarginiii\advance\labelwidth-\labelsep +\topsep 1pt plus 0.5pt minus 0.5pt +\parsep \z@ \partopsep 0.5pt plus 0pt minus 0.5pt +\itemsep \topsep} +\def\@listiv{\leftmargin\leftmarginiv +\labelwidth\leftmarginiv\advance\labelwidth-\labelsep} +\def\@listv{\leftmargin\leftmarginv +\labelwidth\leftmarginv\advance\labelwidth-\labelsep} +\def\@listvi{\leftmargin\leftmarginvi +\labelwidth\leftmarginvi\advance\labelwidth-\labelsep} +\abovedisplayskip 7pt plus2pt minus5pt% +\belowdisplayskip \abovedisplayskip +\abovedisplayshortskip 0pt plus3pt% +\belowdisplayshortskip 4pt plus3pt minus3pt% + +%%%%%% +\setlength{\abovecaptionskip}{4pt}%plus3pt minus3pt}% +\setlength{\belowcaptionskip}{-4pt}%plus3pt minus3pt} +%%%%%% +% Less leading in most fonts (due to the narrow columns) +% The choices were between 1-pt and 1.5-pt leading +\def\normalsize{\@setfontsize\normalsize\@xpt{11}} % 10 point on 11 +\def\small{\@setfontsize\small\@ixpt{10}} % 9 point on 10 +\def\smalll{\@setfontsize\smalll\@viiipt{10}} % 9 point on 9 +\def\footnotesize{\@setfontsize\footnotesize\@ixpt{10}} % 9 point on 10 +\def\scriptsize{\@setfontsize\scriptsize\@viipt{10}} % 7 point on 8 +\def\tiny{\@setfontsize\tiny\@vipt{7}} % 6 point on 7 +\def\large{\@setfontsize\large\@xipt{12}} % 11 point on 12 +\def\Large{\@setfontsize\Large\@xiipt{14}} % 12 point on 14 +\def\LARGE{\@setfontsize\LARGE\@xivpt{16}} % 14 point on 16 +\def\huge{\@setfontsize\huge\@xviipt{20}} % 17 point on 20 +\def\Huge{\@setfontsize\Huge\@xxpt{23}} % 20 point on 23 + +\setlength{\topmargin}{-1.1cm} \addtolength{\textheight}{-0.1cm} +\setlength{\headsep}{1.9cm} +\setlength{\footskip}{1.7cm} + +\renewcommand{\large}{\fontsize{12}{15}\selectfont} +\renewcommand{\Large}{\fontsize{13}{15}\selectfont} +\renewcommand{\normalsize}{\fontsize{10}{11.5}\selectfont} +\renewcommand{\refname}{REFERENCES} + +\newcommand{\F}{\mathcal{F}} +\newcommand{\I}{\mathcal{I}} +\newcommand{\D}{\mathcal{D}} +\newcommand{\T}{\mathcal{T}} +\newcommand{\R}{\mathcal{R}} +\newcommand{\rr}{\mathfrak{r}} +\newcommand{\code}[1]{\textsf{#1}} + +\renewcommand\floatpagefraction{.9} +\renewcommand\topfraction{.9} +\renewcommand\bottomfraction{.9} +\renewcommand\textfraction{.1} \ No newline at end of file diff --git a/abstract.tex b/abstract.tex new file mode 100644 index 0000000..6fbefec --- /dev/null +++ b/abstract.tex @@ -0,0 +1,17 @@ +Chaotic functions are often successfully embedded +into pseudorandom sequence generators. +However even if these generators +can effectively face statistical tests +(thanks to optimized parameters), they may lose +their chaos properties since +they are designed using floating point numbers instead of real ones +numbers. +In a previous work, we had constructed chaos-based PRNGs +defined on a discrete domain. In this context, proofs that are +formally established are preserved during the execution. +We had shown that these generators successfully pass +the most stringent statistical tests +and we had proven that some of them are chaotic. +This work completes this task and shows that +this whole class of PRNGS is chaotic +if and only if some given graphs of iteration are strongly connected. diff --git a/apalike.bst b/apalike.bst new file mode 100644 index 0000000..a7d00ff --- /dev/null +++ b/apalike.bst @@ -0,0 +1,1102 @@ +%NAME: apalike.bst +% BibTeX `apalike' bibliography style (24-Jan-88 version) +% Adapted from the `alpha' style, version 0.99a; for BibTeX version 0.99a. +% Copyright (C) 1988, all rights reserved. +% Copying of this file is allowed, provided that if you make any changes at all +% you name it something other than `apalike.bst'. +% This restriction helps ensure that all copies are identical. +% Differences between this style and `alpha' are generally heralded by a `%'. +% The file btxbst.doc has the documentation for alpha.bst. +% +% This style should be used with the `apalike' LaTeX style (apalike.sty). +% \cite's come out like "(Jones, 1986)" in the text but there are no labels +% in the bibliography, and something like "(1986)" comes out immediately +% after the author. Author (and editor) names appear as last name, comma, +% initials. A `year' field is required for every entry, and so is either +% an author (or in some cases, an editor) field or a key field. +% +% Editorial note: +% Many journals require a style like `apalike', but I strongly, strongly, +% strongly recommend that you not use it if you have a choice---use something +% like `plain' instead. Mary-Claire van Leunen (A Handbook for Scholars, +% Knopf, 1979) argues convincingly that a style like `plain' encourages better +% writing than one like `apalike'. Furthermore the strongest arguments for +% using an author-date style like `apalike'---that it's "the most practical" +% (The Chicago Manual of Style, University of Chicago Press, thirteenth +% edition, 1982, pages 400--401)---fall flat on their face with the new +% computer-typesetting technology. For instance page 401 anachronistically +% states "The chief disadvantage of [a style like `plain'] is that additions +% or deletions cannot be made after the manuscript is typed without changing +% numbers in both text references and list." LaTeX sidesteps the disadvantage. +% +% History: +% 15-sep-86 (SK,OP) Original version, by Susan King and Oren Patashnik. +% 10-nov-86 (OP) Truncated the sort.key$ string to the correct length +% in bib.sort.order to eliminate error message. +% 24-jan-88 (OP) Updated for BibTeX version 0.99a, from alpha.bst 0.99a; +% apalike now sorts by author, then year, then title; +% THIS `apalike' VERSION DOES NOT WORK WITH BIBTEX 0.98i. + +ENTRY + { address + author + booktitle + chapter + edition + editor + howpublished + institution + journal + key +% month not used in apalike + note + number + organization + pages + publisher + school + series + title + type + volume + year + } + {} + { label extra.label sort.label } + +INTEGERS { output.state before.all mid.sentence after.sentence after.block } + +FUNCTION {init.state.consts} +{ #0 'before.all := + #1 'mid.sentence := + #2 'after.sentence := + #3 'after.block := +} + +STRINGS { s t } + +FUNCTION {output.nonnull} +{ 's := + output.state mid.sentence = + { ", " * write$ } + { output.state after.block = + { add.period$ write$ + newline$ + "\newblock " write$ + } + { output.state before.all = + 'write$ + { add.period$ " " * write$ } + if$ + } + if$ + mid.sentence 'output.state := + } + if$ + s +} + +FUNCTION {output} +{ duplicate$ empty$ + 'pop$ + 'output.nonnull + if$ +} + +FUNCTION {output.check} +{ 't := + duplicate$ empty$ + { pop$ "empty " t * " in " * cite$ * warning$ } + 'output.nonnull + if$ +} + +% apalike needs this function because +% the year has special punctuation; +% apalike ignores the month +FUNCTION {output.year.check} +{ year empty$ + { "empty year in " cite$ * warning$ } + { write$ + " (" year * extra.label * ")" * + mid.sentence 'output.state := + } + if$ +} + +FUNCTION {output.bibitem} +{ newline$ + "\bibitem[" write$ + label write$ + "]{" write$ + cite$ write$ + "}" write$ + newline$ + "" + before.all 'output.state := +} + +FUNCTION {fin.entry} +{ add.period$ + write$ + newline$ +} + +FUNCTION {new.block} +{ output.state before.all = + 'skip$ + { after.block 'output.state := } + if$ +} + +FUNCTION {new.sentence} +{ output.state after.block = + 'skip$ + { output.state before.all = + 'skip$ + { after.sentence 'output.state := } + if$ + } + if$ +} + +FUNCTION {not} +{ { #0 } + { #1 } + if$ +} + +FUNCTION {and} +{ 'skip$ + { pop$ #0 } + if$ +} + +FUNCTION {or} +{ { pop$ #1 } + 'skip$ + if$ +} + +FUNCTION {new.block.checkb} +{ empty$ + swap$ empty$ + and + 'skip$ + 'new.block + if$ +} + +FUNCTION {field.or.null} +{ duplicate$ empty$ + { pop$ "" } + 'skip$ + if$ +} + +FUNCTION {emphasize} +{ duplicate$ empty$ + { pop$ "" } + { "{\em " swap$ * "}" * } + if$ +} + +INTEGERS { nameptr namesleft numnames } + +FUNCTION {format.names} +{ 's := + #1 'nameptr := + s num.names$ 'numnames := + numnames 'namesleft := + { namesleft #0 > } + { s nameptr "{vv~}{ll}{, jj}{, f.}" format.name$ 't := % last name first + nameptr #1 > + { namesleft #1 > + { ", " * t * } + { numnames #2 > + { "," * } + 'skip$ + if$ + t "others" = + { " et~al." * } + { " and " * t * } + if$ + } + if$ + } + 't + if$ + nameptr #1 + 'nameptr := + namesleft #1 - 'namesleft := + } + while$ +} + +FUNCTION {format.authors} +{ author empty$ + { "" } + { author format.names } + if$ +} + +FUNCTION {format.key} % this function is just for apalike +{ empty$ + { key field.or.null } + { "" } + if$ +} + +FUNCTION {format.editors} +{ editor empty$ + { "" } + { editor format.names + editor num.names$ #1 > + { ", editors" * } + { ", editor" * } + if$ + } + if$ +} + +FUNCTION {format.title} +{ title empty$ + { "" } + { title "t" change.case$ } + if$ +} + +FUNCTION {n.dashify} +{ 't := + "" + { t empty$ not } + { t #1 #1 substring$ "-" = + { t #1 #2 substring$ "--" = not + { "--" * + t #2 global.max$ substring$ 't := + } + { { t #1 #1 substring$ "-" = } + { "-" * + t #2 global.max$ substring$ 't := + } + while$ + } + if$ + } + { t #1 #1 substring$ * + t #2 global.max$ substring$ 't := + } + if$ + } + while$ +} + +FUNCTION {format.btitle} +{ title emphasize +} + +FUNCTION {tie.or.space.connect} +{ duplicate$ text.length$ #3 < + { "~" } + { " " } + if$ + swap$ * * +} + +FUNCTION {either.or.check} +{ empty$ + 'pop$ + { "can't use both " swap$ * " fields in " * cite$ * warning$ } + if$ +} + +FUNCTION {format.bvolume} +{ volume empty$ + { "" } + { "volume" volume tie.or.space.connect + series empty$ + 'skip$ + { " of " * series emphasize * } + if$ + "volume and number" number either.or.check + } + if$ +} + +FUNCTION {format.number.series} +{ volume empty$ + { number empty$ + { series field.or.null } + { output.state mid.sentence = + { "number" } + { "Number" } + if$ + number tie.or.space.connect + series empty$ + { "there's a number but no series in " cite$ * warning$ } + { " in " * series * } + if$ + } + if$ + } + { "" } + if$ +} + +FUNCTION {format.edition} +{ edition empty$ + { "" } + { output.state mid.sentence = + { edition "l" change.case$ " edition" * } + { edition "t" change.case$ " edition" * } + if$ + } + if$ +} + +INTEGERS { multiresult } + +FUNCTION {multi.page.check} +{ 't := + #0 'multiresult := + { multiresult not + t empty$ not + and + } + { t #1 #1 substring$ + duplicate$ "-" = + swap$ duplicate$ "," = + swap$ "+" = + or or + { #1 'multiresult := } + { t #2 global.max$ substring$ 't := } + if$ + } + while$ + multiresult +} + +FUNCTION {format.pages} +{ pages empty$ + { "" } + { pages multi.page.check + { "pages" pages n.dashify tie.or.space.connect } + { "page" pages tie.or.space.connect } + if$ + } + if$ +} + +FUNCTION {format.vol.num.pages} +{ volume field.or.null + number empty$ + 'skip$ + { "(" number * ")" * * + volume empty$ + { "there's a number but no volume in " cite$ * warning$ } + 'skip$ + if$ + } + if$ + pages empty$ + 'skip$ + { duplicate$ empty$ + { pop$ format.pages } + { ":" * pages n.dashify * } + if$ + } + if$ +} + +FUNCTION {format.chapter.pages} +{ chapter empty$ + 'format.pages + { type empty$ + { "chapter" } + { type "l" change.case$ } + if$ + chapter tie.or.space.connect + pages empty$ + 'skip$ + { ", " * format.pages * } + if$ + } + if$ +} + +FUNCTION {format.in.ed.booktitle} +{ booktitle empty$ + { "" } + { editor empty$ + { "In " booktitle emphasize * } + { "In " format.editors * ", " * booktitle emphasize * } + if$ + } + if$ +} + +FUNCTION {format.thesis.type} +{ type empty$ + 'skip$ + { pop$ + type "t" change.case$ + } + if$ +} + +FUNCTION {format.tr.number} +{ type empty$ + { "Technical Report" } + 'type + if$ + number empty$ + { "t" change.case$ } + { number tie.or.space.connect } + if$ +} + +FUNCTION {format.article.crossref} +{ "In" % this is for apalike + " \cite{" * crossref * "}" * +} + +FUNCTION {format.book.crossref} +{ volume empty$ + { "empty volume in " cite$ * "'s crossref of " * crossref * warning$ + "In " + } + { "Volume" volume tie.or.space.connect + " of " * + } + if$ + "\cite{" * crossref * "}" * % this is for apalike +} + +FUNCTION {format.incoll.inproc.crossref} +{ "In" % this is for apalike + " \cite{" * crossref * "}" * +} + +FUNCTION {article} +{ output.bibitem + format.authors "author" output.check + author format.key output % special for + output.year.check % apalike + new.block + format.title "title" output.check + new.block + crossref missing$ + { journal emphasize "journal" output.check + format.vol.num.pages output + } + { format.article.crossref output.nonnull + format.pages output + } + if$ + new.block + note output + fin.entry +} + +FUNCTION {book} +{ output.bibitem + author empty$ + { format.editors "author and editor" output.check + editor format.key output + } + { format.authors output.nonnull + crossref missing$ + { "author and editor" editor either.or.check } + 'skip$ + if$ + } + if$ + output.year.check % special for apalike + new.block + format.btitle "title" output.check + crossref missing$ + { format.bvolume output + new.block + format.number.series output + new.sentence + publisher "publisher" output.check + address output + } + { new.block + format.book.crossref output.nonnull + } + if$ + format.edition output + new.block + note output + fin.entry +} + +FUNCTION {booklet} +{ output.bibitem + format.authors output + author format.key output % special for + output.year.check % apalike + new.block + format.title "title" output.check + new.block + howpublished output + address output + new.block + note output + fin.entry +} + +FUNCTION {inbook} +{ output.bibitem + author empty$ + { format.editors "author and editor" output.check + editor format.key output + } + { format.authors output.nonnull + crossref missing$ + { "author and editor" editor either.or.check } + 'skip$ + if$ + } + if$ + output.year.check % special for apalike + new.block + format.btitle "title" output.check + crossref missing$ + { format.bvolume output + format.chapter.pages "chapter and pages" output.check + new.block + format.number.series output + new.sentence + publisher "publisher" output.check + address output + } + { format.chapter.pages "chapter and pages" output.check + new.block + format.book.crossref output.nonnull + } + if$ + format.edition output + new.block + note output + fin.entry +} + +FUNCTION {incollection} +{ output.bibitem + format.authors "author" output.check + author format.key output % special for + output.year.check % apalike + new.block + format.title "title" output.check + new.block + crossref missing$ + { format.in.ed.booktitle "booktitle" output.check + format.bvolume output + format.number.series output + format.chapter.pages output + new.sentence + publisher "publisher" output.check + address output + format.edition output + } + { format.incoll.inproc.crossref output.nonnull + format.chapter.pages output + } + if$ + new.block + note output + fin.entry +} + +FUNCTION {inproceedings} +{ output.bibitem + format.authors "author" output.check + author format.key output % special for + output.year.check % apalike + new.block + format.title "title" output.check + new.block + crossref missing$ + { format.in.ed.booktitle "booktitle" output.check + format.bvolume output + format.number.series output + format.pages output + address output % for apalike + new.sentence % there's no year + organization output % here so things + publisher output % are simpler + } + { format.incoll.inproc.crossref output.nonnull + format.pages output + } + if$ + new.block + note output + fin.entry +} + +FUNCTION {conference} { inproceedings } + +FUNCTION {manual} +{ output.bibitem + format.authors output + author format.key output % special for + output.year.check % apalike + new.block + format.btitle "title" output.check + organization address new.block.checkb + organization output + address output + format.edition output + new.block + note output + fin.entry +} + +FUNCTION {mastersthesis} +{ output.bibitem + format.authors "author" output.check + author format.key output % special for + output.year.check % apalike + new.block + format.title "title" output.check + new.block + "Master's thesis" format.thesis.type output.nonnull + school "school" output.check + address output + new.block + note output + fin.entry +} + +FUNCTION {misc} +{ output.bibitem + format.authors output + author format.key output % special for + output.year.check % apalike + new.block + format.title output + new.block + howpublished output + new.block + note output + fin.entry +} + +FUNCTION {phdthesis} +{ output.bibitem + format.authors "author" output.check + author format.key output % special for + output.year.check % apalike + new.block + format.btitle "title" output.check + new.block + "PhD thesis" format.thesis.type output.nonnull + school "school" output.check + address output + new.block + note output + fin.entry +} + +FUNCTION {proceedings} +{ output.bibitem + format.editors output + editor format.key output % special for + output.year.check % apalike + new.block + format.btitle "title" output.check + format.bvolume output + format.number.series output + address output % for apalike + new.sentence % we always output + organization output % a nonempty organization + publisher output % here + new.block + note output + fin.entry +} + +FUNCTION {techreport} +{ output.bibitem + format.authors "author" output.check + author format.key output % special for + output.year.check % apalike + new.block + format.title "title" output.check + new.block + format.tr.number output.nonnull + institution "institution" output.check + address output + new.block + note output + fin.entry +} + +FUNCTION {unpublished} +{ output.bibitem + format.authors "author" output.check + author format.key output % special for + output.year.check % apalike + new.block + format.title "title" output.check + new.block + note "note" output.check + fin.entry +} + +FUNCTION {default.type} { misc } + +MACRO {jan} {"January"} + +MACRO {feb} {"February"} + +MACRO {mar} {"March"} + +MACRO {apr} {"April"} + +MACRO {may} {"May"} + +MACRO {jun} {"June"} + +MACRO {jul} {"July"} + +MACRO {aug} {"August"} + +MACRO {sep} {"September"} + +MACRO {oct} {"October"} + +MACRO {nov} {"November"} + +MACRO {dec} {"December"} + +MACRO {acmcs} {"ACM Computing Surveys"} + +MACRO {acta} {"Acta Informatica"} + +MACRO {cacm} {"Communications of the ACM"} + +MACRO {ibmjrd} {"IBM Journal of Research and Development"} + +MACRO {ibmsj} {"IBM Systems Journal"} + +MACRO {ieeese} {"IEEE Transactions on Software Engineering"} + +MACRO {ieeetc} {"IEEE Transactions on Computers"} + +MACRO {ieeetcad} + {"IEEE Transactions on Computer-Aided Design of Integrated Circuits"} + +MACRO {ipl} {"Information Processing Letters"} + +MACRO {jacm} {"Journal of the ACM"} + +MACRO {jcss} {"Journal of Computer and System Sciences"} + +MACRO {scp} {"Science of Computer Programming"} + +MACRO {sicomp} {"SIAM Journal on Computing"} + +MACRO {tocs} {"ACM Transactions on Computer Systems"} + +MACRO {tods} {"ACM Transactions on Database Systems"} + +MACRO {tog} {"ACM Transactions on Graphics"} + +MACRO {toms} {"ACM Transactions on Mathematical Software"} + +MACRO {toois} {"ACM Transactions on Office Information Systems"} + +MACRO {toplas} {"ACM Transactions on Programming Languages and Systems"} + +MACRO {tcs} {"Theoretical Computer Science"} + +READ + +FUNCTION {sortify} +{ purify$ + "l" change.case$ +} + +INTEGERS { len } + +FUNCTION {chop.word} +{ 's := + 'len := + s #1 len substring$ = + { s len #1 + global.max$ substring$ } + 's + if$ +} + +% There are three apalike cases: one person (Jones), +% two (Jones and de~Bruijn), and more (Jones et~al.). +% This function is much like format.crossref.editors. +% +FUNCTION {format.lab.names} +{ 's := + s #1 "{vv~}{ll}" format.name$ + s num.names$ duplicate$ + #2 > + { pop$ " et~al." * } + { #2 < + 'skip$ + { s #2 "{ff }{vv }{ll}{ jj}" format.name$ "others" = + { " et~al." * } + { " and " * s #2 "{vv~}{ll}" format.name$ * } + if$ + } + if$ + } + if$ +} + +FUNCTION {author.key.label} +{ author empty$ + { key empty$ + { cite$ #1 #3 substring$ } + 'key % apalike uses the whole key + if$ + } + { author format.lab.names } + if$ +} + +FUNCTION {author.editor.key.label} +{ author empty$ + { editor empty$ + { key empty$ + { cite$ #1 #3 substring$ } + 'key % apalike uses the whole key + if$ + } + { editor format.lab.names } + if$ + } + { author format.lab.names } + if$ +} + +FUNCTION {editor.key.label} +{ editor empty$ + { key empty$ + { cite$ #1 #3 substring$ } + 'key % apalike uses the whole key, no organization + if$ + } + { editor format.lab.names } + if$ +} + +FUNCTION {calc.label} +{ type$ "book" = + type$ "inbook" = + or + 'author.editor.key.label + { type$ "proceedings" = + 'editor.key.label % apalike ignores organization + 'author.key.label % for labeling and sorting + if$ + } + if$ + ", " % these three lines are + * % for apalike, which + year field.or.null purify$ #-1 #4 substring$ % uses all four digits + * + 'label := +} + +FUNCTION {sort.format.names} +{ 's := + #1 'nameptr := + "" + s num.names$ 'numnames := + numnames 'namesleft := + { namesleft #0 > } + { nameptr #1 > + { " " * } + 'skip$ + if$ % apalike uses initials + s nameptr "{vv{ } }{ll{ }}{ f{ }}{ jj{ }}" format.name$ 't := % <= here + nameptr numnames = t "others" = and + { "et al" * } + { t sortify * } + if$ + nameptr #1 + 'nameptr := + namesleft #1 - 'namesleft := + } + while$ +} + +FUNCTION {sort.format.title} +{ 't := + "A " #2 + "An " #3 + "The " #4 t chop.word + chop.word + chop.word + sortify + #1 global.max$ substring$ +} + +FUNCTION {author.sort} +{ author empty$ + { key empty$ + { "to sort, need author or key in " cite$ * warning$ + "" + } + { key sortify } + if$ + } + { author sort.format.names } + if$ +} + +FUNCTION {author.editor.sort} +{ author empty$ + { editor empty$ + { key empty$ + { "to sort, need author, editor, or key in " cite$ * warning$ + "" + } + { key sortify } + if$ + } + { editor sort.format.names } + if$ + } + { author sort.format.names } + if$ +} + +FUNCTION {editor.sort} +{ editor empty$ + { key empty$ + { "to sort, need editor or key in " cite$ * warning$ + "" + } + { key sortify } + if$ + } + { editor sort.format.names } + if$ +} + +% apalike uses two sorting passes; the first one sets the +% labels so that the `a's, `b's, etc. can be computed; +% the second pass puts the references in "correct" order. +% The presort function is for the first pass. It computes +% label, sort.label, and title, and then concatenates. +FUNCTION {presort} +{ calc.label + label sortify + " " + * + type$ "book" = + type$ "inbook" = + or + 'author.editor.sort + { type$ "proceedings" = + 'editor.sort + 'author.sort + if$ + } + if$ + #1 entry.max$ substring$ % for + 'sort.label := % apalike + sort.label % style + * + " " + * + title field.or.null + sort.format.title + * + #1 entry.max$ substring$ + 'sort.key$ := +} + +ITERATE {presort} + +SORT % by label, sort.label, title---for final label calculation + +STRINGS { last.label next.extra } % apalike labels are only for the text; + +INTEGERS { last.extra.num } % there are none in the bibliography + +FUNCTION {initialize.extra.label.stuff} % and hence there is no `longest.label' +{ #0 int.to.chr$ 'last.label := + "" 'next.extra := + #0 'last.extra.num := +} + +FUNCTION {forward.pass} +{ last.label label = + { last.extra.num #1 + 'last.extra.num := + last.extra.num int.to.chr$ 'extra.label := + } + { "a" chr.to.int$ 'last.extra.num := + "" 'extra.label := + label 'last.label := + } + if$ +} + +FUNCTION {reverse.pass} +{ next.extra "b" = + { "a" 'extra.label := } + 'skip$ + if$ + label extra.label * 'label := + extra.label 'next.extra := +} + +EXECUTE {initialize.extra.label.stuff} + +ITERATE {forward.pass} + +REVERSE {reverse.pass} + +% Now that the label is right we sort for real, +% on sort.label then year then title. This is +% for the second sorting pass. +FUNCTION {bib.sort.order} +{ sort.label + " " + * + year field.or.null sortify + * + " " + * + title field.or.null + sort.format.title + * + #1 entry.max$ substring$ + 'sort.key$ := +} + +ITERATE {bib.sort.order} + +SORT % by sort.label, year, title---giving final bibliography order + +FUNCTION {begin.bib} +{ preamble$ empty$ % no \etalchar in apalike + 'skip$ + { preamble$ write$ newline$ } + if$ + "\begin{thebibliography}{}" write$ newline$ % no labels in apalike +} + +EXECUTE {begin.bib} + +EXECUTE {init.state.consts} + +ITERATE {call.type$} + +FUNCTION {end.bib} +{ newline$ + "\end{thebibliography}" write$ newline$ +} + +EXECUTE {end.bib} diff --git a/apalike.sty b/apalike.sty new file mode 100644 index 0000000..09863b7 --- /dev/null +++ b/apalike.sty @@ -0,0 +1,31 @@ +\def\@cite#1#2{(#1\if@tempswa , #2\fi)} +\def\@biblabel#1{} + +\newlength{\bibhang} +\setlength{\bibhang}{2em} + +\@ifundefined{chapter}{\def\thebibliography#1{\section*{REFERENCES\@mkboth + {REFERENCES}{REFERENCES}}\list + {\relax}{\setlength{\labelsep}{0em} + \setlength{\itemindent}{-\bibhang} + \setlength{\leftmargin}{\bibhang}} + \itemsep 0pt\parsep 0pt + \def\newblock{\hskip .11em plus .33em minus .07em} + \sloppy\clubpenalty4000\widowpenalty4000 + \sfcode`\.=1000\relax}}% +{\def\thebibliography#1{\chapter*{Bibliography\@mkboth + {BIBLIOGRAPHY}{BIBLIOGRAPHY}}\list + {\relax}{\setlength{\labelsep}{0em} + \setlength{\itemindent}{-\bibhang} + \setlength{\leftmargin}{\bibhang}} + \itemsep 0pt\parsep 0pt + \def\newblock{\hskip .11em plus .33em minus .07em} + \sloppy\clubpenalty4000\widowpenalty4000 + \sfcode`\.=1000\relax}} + +\def\@citex[#1]#2{\if@filesw\immediate\write\@auxout{\string\citation{#2}}\fi + \def\@citea{}\@cite{\@for\@citeb:=#2\do + {\@citea\def\@citea{; }\@ifundefined + {b@\@citeb}{{\bf ?}\@warning + {Citation `\@citeb' on page \thepage \space undefined}}% +{\csname b@\@citeb\endcsname}}}{#1}} diff --git a/article.cls b/article.cls new file mode 100644 index 0000000..512b8a4 --- /dev/null +++ b/article.cls @@ -0,0 +1,642 @@ +%% +%% This is file `article.cls', +%% generated with the docstrip utility. +%% +%% The original source files were: +%% +%% classes.dtx (with options: `article') +%% +%% This is a generated file. +%% +%% Copyright 1993 1994 1995 1996 1997 1998 1999 2000 +%% The LaTeX3 Project and any individual authors listed elsewhere +%% in this file. +%% +%% This file was generated from file(s) of the LaTeX base system. +%% -------------------------------------------------------------- +%% +%% It may be distributed and/or modified under the +%% conditions of the LaTeX Project Public License, either version 1.2 +%% of this license or (at your option) any later version. +%% The latest version of this license is in +%% http://www.latex-project.org/lppl.txt +%% and version 1.2 or later is part of all distributions of LaTeX +%% version 1999/12/01 or later. +%% +%% This file may only be distributed together with a copy of the LaTeX +%% base system. You may however distribute the LaTeX base system without +%% such generated files. +%% +%% The list of all files belonging to the LaTeX base distribution is +%% given in the file `manifest.txt'. See also `legal.txt' for additional +%% information. +%% +%% \CharacterTable +%% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z +%% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z +%% Digits \0\1\2\3\4\5\6\7\8\9 +%% Exclamation \! Double quote \" Hash (number) \# +%% Dollar \$ Percent \% Ampersand \& +%% Acute accent \' Left paren \( Right paren \) +%% Asterisk \* Plus \+ Comma \, +%% Minus \- Point \. Solidus \/ +%% Colon \: Semicolon \; Less than \< +%% Equals \= Greater than \> Question mark \? +%% Commercial at \@ Left bracket \[ Backslash \\ +%% Right bracket \] Circumflex \^ Underscore \_ +%% Grave accent \` Left brace \{ Vertical bar \| +%% Right brace \} Tilde \~} +\NeedsTeXFormat{LaTeX2e}[1995/12/01] +\ProvidesClass{article} + [2000/05/19 v1.4b + Standard LaTeX document class] +\newcommand\@ptsize{} +\newif\if@restonecol +\newif\if@titlepage +\@titlepagefalse +\if@compatibility\else +\DeclareOption{a4paper} + {\setlength\paperheight {297mm}% + \setlength\paperwidth {210mm}} +\DeclareOption{a5paper} + {\setlength\paperheight {210mm}% + \setlength\paperwidth {148mm}} +\DeclareOption{b5paper} + {\setlength\paperheight {250mm}% + \setlength\paperwidth {176mm}} +\DeclareOption{letterpaper} + {\setlength\paperheight {11in}% + \setlength\paperwidth {8.5in}} +\DeclareOption{legalpaper} + {\setlength\paperheight {14in}% + \setlength\paperwidth {8.5in}} +\DeclareOption{executivepaper} + {\setlength\paperheight {10.5in}% + \setlength\paperwidth {7.25in}} +\DeclareOption{landscape} + {\setlength\@tempdima {\paperheight}% + \setlength\paperheight {\paperwidth}% + \setlength\paperwidth {\@tempdima}} +\fi +\if@compatibility + \renewcommand\@ptsize{0} +\else +\DeclareOption{10pt}{\renewcommand\@ptsize{0}} +\fi +\DeclareOption{11pt}{\renewcommand\@ptsize{1}} +\DeclareOption{12pt}{\renewcommand\@ptsize{2}} +\if@compatibility\else +\DeclareOption{oneside}{\@twosidefalse \@mparswitchfalse} +\fi +\DeclareOption{twoside}{\@twosidetrue \@mparswitchtrue} +\DeclareOption{draft}{\setlength\overfullrule{5pt}} +\if@compatibility\else +\DeclareOption{final}{\setlength\overfullrule{0pt}} +\fi +\DeclareOption{titlepage}{\@titlepagetrue} +\if@compatibility\else +\DeclareOption{notitlepage}{\@titlepagefalse} +\fi +\if@compatibility\else +\DeclareOption{onecolumn}{\@twocolumnfalse} +\fi +\DeclareOption{twocolumn}{\@twocolumntrue} +\DeclareOption{leqno}{\input{leqno.clo}} +\DeclareOption{fleqn}{\input{fleqn.clo}} +\DeclareOption{openbib}{% + \AtEndOfPackage{% + \renewcommand\@openbib@code{% + \advance\leftmargin\bibindent + \itemindent -\bibindent + \listparindent \itemindent + \parsep \z@ + }% + \renewcommand\newblock{\par}}% +} +\ExecuteOptions{letterpaper,10pt,oneside,onecolumn,final} +\ProcessOptions +\input{size1\@ptsize.clo} +\setlength\lineskip{1\p@} +\setlength\normallineskip{1\p@} +\renewcommand\baselinestretch{} +\setlength\parskip{0\p@ \@plus \p@} +\@lowpenalty 51 +\@medpenalty 151 +\@highpenalty 301 +\setcounter{topnumber}{2} +\renewcommand\topfraction{.7} +\setcounter{bottomnumber}{1} +\renewcommand\bottomfraction{.3} +\setcounter{totalnumber}{3} +\renewcommand\textfraction{.2} +\renewcommand\floatpagefraction{.5} +\setcounter{dbltopnumber}{2} +\renewcommand\dbltopfraction{.7} +\renewcommand\dblfloatpagefraction{.5} +\if@twoside + \def\ps@headings{% + \let\@oddfoot\@empty\let\@evenfoot\@empty + \def\@evenhead{\thepage\hfil\slshape\leftmark}% + \def\@oddhead{{\slshape\rightmark}\hfil\thepage}% + \let\@mkboth\markboth + \def\sectionmark##1{% + \markboth {\MakeUppercase{% + \ifnum \c@secnumdepth >\z@ + \thesection\quad + \fi + ##1}}{}}% + \def\subsectionmark##1{% + \markright {% + \ifnum \c@secnumdepth >\@ne + \thesubsection\quad + \fi + ##1}}} +\else + \def\ps@headings{% + \let\@oddfoot\@empty + \def\@oddhead{{\slshape\rightmark}\hfil\thepage}% + \let\@mkboth\markboth + \def\sectionmark##1{% + \markright {\MakeUppercase{% + \ifnum \c@secnumdepth >\m@ne + \thesection\quad + \fi + ##1}}}} +\fi +\def\ps@myheadings{% + \let\@oddfoot\@empty\let\@evenfoot\@empty + \def\@evenhead{\thepage\hfil\slshape\leftmark}% + \def\@oddhead{{\slshape\rightmark}\hfil\thepage}% + \let\@mkboth\@gobbletwo + \let\sectionmark\@gobble + \let\subsectionmark\@gobble + } + \if@titlepage + \newcommand\maketitle{\begin{titlepage}% + \let\footnotesize\small + \let\footnoterule\relax + \let \footnote \thanks + \null\vfil + \vskip 60\p@ + \begin{center}% + {\LARGE \@title \par}% + \vskip 3em% + {\large + \lineskip .75em% + \begin{tabular}[t]{c}% + \@author + \end{tabular}\par}% + \vskip 1.5em% + {\large \@date \par}% % Set date in \large size. + \end{center}\par + \@thanks + \vfil\null + \end{titlepage}% + \setcounter{footnote}{0}% + \global\let\thanks\relax + \global\let\maketitle\relax + \global\let\@thanks\@empty + \global\let\@author\@empty + \global\let\@date\@empty + \global\let\@title\@empty + \global\let\title\relax + \global\let\author\relax + \global\let\date\relax + \global\let\and\relax +} +\else +\newcommand\maketitle{\par + \begingroup + \renewcommand\thefootnote{\@fnsymbol\c@footnote}% + \def\@makefnmark{\rlap{\@textsuperscript{\normalfont\@thefnmark}}}% + \long\def\@makefntext##1{\parindent 1em\noindent + \hb@xt@1.8em{% + \hss\@textsuperscript{\normalfont\@thefnmark}}##1}% + \if@twocolumn + \ifnum \col@number=\@ne + \@maketitle + \else + \twocolumn[\@maketitle]% + \fi + \else + \newpage + \global\@topnum\z@ % Prevents figures from going at top of page. + \@maketitle + \fi + \thispagestyle{plain}\@thanks + \endgroup + \setcounter{footnote}{0}% + \global\let\thanks\relax + \global\let\maketitle\relax + \global\let\@maketitle\relax + \global\let\@thanks\@empty + \global\let\@author\@empty + \global\let\@date\@empty + \global\let\@title\@empty + \global\let\title\relax + \global\let\author\relax + \global\let\date\relax + \global\let\and\relax +} +\def\@maketitle{% + \newpage + \null + \vskip 2em% + \begin{center}% + \let \footnote \thanks + {\LARGE \@title \par}% + \vskip 1.5em% + {\large + \lineskip .5em% + \begin{tabular}[t]{c}% + \@author + \end{tabular}\par}% + \vskip 1em% + {\large \@date}% + \end{center}% + \par + \vskip 1.5em} +\fi +\setcounter{secnumdepth}{3} +\newcounter {part} +\newcounter {section} +\newcounter {subsection}[section] +\newcounter {subsubsection}[subsection] +\newcounter {paragraph}[subsubsection] +\newcounter {subparagraph}[paragraph] +\renewcommand \thepart {\@Roman\c@part} +\renewcommand \thesection {\@arabic\c@section} +\renewcommand\thesubsection {\thesection.\@arabic\c@subsection} +\renewcommand\thesubsubsection{\thesubsection .\@arabic\c@subsubsection} +\renewcommand\theparagraph {\thesubsubsection.\@arabic\c@paragraph} +\renewcommand\thesubparagraph {\theparagraph.\@arabic\c@subparagraph} +\newcommand\part{% + \if@noskipsec \leavevmode \fi + \par + \addvspace{4ex}% + \@afterindentfalse + \secdef\@part\@spart} + +\def\@part[#1]#2{% + \ifnum \c@secnumdepth >\m@ne + \refstepcounter{part}% + \addcontentsline{toc}{part}{\thepart\hspace{1em}#1}% + \else + \addcontentsline{toc}{part}{#1}% + \fi + {\parindent \z@ \raggedright + \interlinepenalty \@M + \normalfont + \ifnum \c@secnumdepth >\m@ne + \Large\bfseries \partname~\thepart + \par\nobreak + \fi + \huge \bfseries #2% + \markboth{}{}\par}% + \nobreak + \vskip 3ex + \@afterheading} +\def\@spart#1{% + {\parindent \z@ \raggedright + \interlinepenalty \@M + \normalfont + \huge \bfseries #1\par}% + \nobreak + \vskip 3ex + \@afterheading} +\newcommand\section{\@startsection {section}{1}{\z@}% + {-3.5ex \@plus -1ex \@minus -.2ex}% + {2.3ex \@plus.2ex}% + {\normalfont\Large\bfseries}} +\newcommand\subsection{\@startsection{subsection}{2}{\z@}% + {-3.25ex\@plus -1ex \@minus -.2ex}% + {1.5ex \@plus .2ex}% + {\normalfont\large\bfseries}} +\newcommand\subsubsection{\@startsection{subsubsection}{3}{\z@}% + {-3.25ex\@plus -1ex \@minus -.2ex}% + {1.5ex \@plus .2ex}% + {\normalfont\normalsize\bfseries}} +\newcommand\paragraph{\@startsection{paragraph}{4}{\z@}% + {3.25ex \@plus1ex \@minus.2ex}% + {-1em}% + {\normalfont\normalsize\bfseries}} +\newcommand\subparagraph{\@startsection{subparagraph}{5}{\parindent}% + {3.25ex \@plus1ex \@minus .2ex}% + {-1em}% + {\normalfont\normalsize\bfseries}} +\if@twocolumn + \setlength\leftmargini {2em} +\else + \setlength\leftmargini {2.5em} +\fi +\leftmargin \leftmargini +\setlength\leftmarginii {2.2em} +\setlength\leftmarginiii {1.87em} +\setlength\leftmarginiv {1.7em} +\if@twocolumn + \setlength\leftmarginv {.5em} + \setlength\leftmarginvi {.5em} +\else + \setlength\leftmarginv {1em} + \setlength\leftmarginvi {1em} +\fi +\setlength \labelsep {.5em} +\setlength \labelwidth{\leftmargini} +\addtolength\labelwidth{-\labelsep} +\@beginparpenalty -\@lowpenalty +\@endparpenalty -\@lowpenalty +\@itempenalty -\@lowpenalty +\renewcommand\theenumi{\@arabic\c@enumi} +\renewcommand\theenumii{\@alph\c@enumii} +\renewcommand\theenumiii{\@roman\c@enumiii} +\renewcommand\theenumiv{\@Alph\c@enumiv} +\newcommand\labelenumi{\theenumi.} +\newcommand\labelenumii{(\theenumii)} +\newcommand\labelenumiii{\theenumiii.} +\newcommand\labelenumiv{\theenumiv.} +\renewcommand\p@enumii{\theenumi} +\renewcommand\p@enumiii{\theenumi(\theenumii)} +\renewcommand\p@enumiv{\p@enumiii\theenumiii} +\newcommand\labelitemi{\textbullet} +\newcommand\labelitemii{\normalfont\bfseries \textendash} +\newcommand\labelitemiii{\textasteriskcentered} +\newcommand\labelitemiv{\textperiodcentered} +\newenvironment{description} + {\list{}{\labelwidth\z@ \itemindent-\leftmargin + \let\makelabel\descriptionlabel}} + {\endlist} +\newcommand*\descriptionlabel[1]{\hspace\labelsep + \normalfont\bfseries #1} +\if@titlepage + \newenvironment{abstract}{% + \titlepage + \null\vfil + \@beginparpenalty\@lowpenalty + \begin{center}% + \bfseries \abstractname + \@endparpenalty\@M + \end{center}}% + {\par\vfil\null\endtitlepage} +\else + \newenvironment{abstract}{% + \if@twocolumn + \section*{\abstractname}% + \else + \small + \begin{center}% + {\bfseries \abstractname\vspace{-.5em}\vspace{\z@}}% + \end{center}% + \quotation + \fi} + {\if@twocolumn\else\endquotation\fi} +\fi +\newenvironment{verse} + {\let\\\@centercr + \list{}{\itemsep \z@ + \itemindent -1.5em% + \listparindent\itemindent + \rightmargin \leftmargin + \advance\leftmargin 1.5em}% + \item\relax} + {\endlist} +\newenvironment{quotation} + {\list{}{\listparindent 1.5em% + \itemindent \listparindent + \rightmargin \leftmargin + \parsep \z@ \@plus\p@}% + \item\relax} + {\endlist} +\newenvironment{quote} + {\list{}{\rightmargin\leftmargin}% + \item\relax} + {\endlist} +\if@compatibility +\newenvironment{titlepage} + {% + \if@twocolumn + \@restonecoltrue\onecolumn + \else + \@restonecolfalse\newpage + \fi + \thispagestyle{empty}% + \setcounter{page}\z@ + }% + {\if@restonecol\twocolumn \else \newpage \fi + } +\else +\newenvironment{titlepage} + {% + \if@twocolumn + \@restonecoltrue\onecolumn + \else + \@restonecolfalse\newpage + \fi + \thispagestyle{empty}% + \setcounter{page}\@ne + }% + {\if@restonecol\twocolumn \else \newpage \fi + \if@twoside\else + \setcounter{page}\@ne + \fi + } +\fi +\newcommand\appendix{\par + \setcounter{section}{0}% + \setcounter{subsection}{0}% + \gdef\thesection{\@Alph\c@section}} +\setlength\arraycolsep{5\p@} +\setlength\tabcolsep{6\p@} +\setlength\arrayrulewidth{.4\p@} +\setlength\doublerulesep{2\p@} +\setlength\tabbingsep{\labelsep} +\skip\@mpfootins = \skip\footins +\setlength\fboxsep{3\p@} +\setlength\fboxrule{.4\p@} +\renewcommand \theequation {\@arabic\c@equation} +\newcounter{figure} +\renewcommand \thefigure {\@arabic\c@figure} +\def\fps@figure{tbp} +\def\ftype@figure{1} +\def\ext@figure{lof} +\def\fnum@figure{\figurename~\thefigure} +\newenvironment{figure} + {\@float{figure}} + {\end@float} +\newenvironment{figure*} + {\@dblfloat{figure}} + {\end@dblfloat} +\newcounter{table} +\renewcommand\thetable{\@arabic\c@table} +\def\fps@table{tbp} +\def\ftype@table{2} +\def\ext@table{lot} +\def\fnum@table{\tablename~\thetable} +\newenvironment{table} + {\@float{table}} + {\end@float} +\newenvironment{table*} + {\@dblfloat{table}} + {\end@dblfloat} +\newlength\abovecaptionskip +\newlength\belowcaptionskip +\setlength\abovecaptionskip{10\p@} +\setlength\belowcaptionskip{0\p@} +\long\def\@makecaption#1#2{% + \vskip\abovecaptionskip + \sbox\@tempboxa{#1: #2}% + \ifdim \wd\@tempboxa >\hsize + #1: #2\par + \else + \global \@minipagefalse + \hb@xt@\hsize{\hfil\box\@tempboxa\hfil}% + \fi + \vskip\belowcaptionskip} +\DeclareOldFontCommand{\rm}{\normalfont\rmfamily}{\mathrm} +\DeclareOldFontCommand{\sf}{\normalfont\sffamily}{\mathsf} +\DeclareOldFontCommand{\tt}{\normalfont\ttfamily}{\mathtt} +\DeclareOldFontCommand{\bf}{\normalfont\bfseries}{\mathbf} +\DeclareOldFontCommand{\it}{\normalfont\itshape}{\mathit} +\DeclareOldFontCommand{\sl}{\normalfont\slshape}{\@nomath\sl} +\DeclareOldFontCommand{\sc}{\normalfont\scshape}{\@nomath\sc} +\DeclareRobustCommand*\cal{\@fontswitch\relax\mathcal} +\DeclareRobustCommand*\mit{\@fontswitch\relax\mathnormal} +\newcommand\@pnumwidth{1.55em} +\newcommand\@tocrmarg{2.55em} +\newcommand\@dotsep{4.5} +\setcounter{tocdepth}{3} +\newcommand\tableofcontents{% + \section*{\contentsname + \@mkboth{% + \MakeUppercase\contentsname}{\MakeUppercase\contentsname}}% + \@starttoc{toc}% + } +\newcommand*\l@part[2]{% + \ifnum \c@tocdepth >-2\relax + \addpenalty\@secpenalty + \addvspace{2.25em \@plus\p@}% + \begingroup + \parindent \z@ \rightskip \@pnumwidth + \parfillskip -\@pnumwidth + {\leavevmode + \large \bfseries #1\hfil \hb@xt@\@pnumwidth{\hss #2}}\par + \nobreak + \if@compatibility + \global\@nobreaktrue + \everypar{\global\@nobreakfalse\everypar{}}% + \fi + \endgroup + \fi} +\newcommand*\l@section[2]{% + \ifnum \c@tocdepth >\z@ + \addpenalty\@secpenalty + \addvspace{1.0em \@plus\p@}% + \setlength\@tempdima{1.5em}% + \begingroup + \parindent \z@ \rightskip \@pnumwidth + \parfillskip -\@pnumwidth + \leavevmode \bfseries + \advance\leftskip\@tempdima + \hskip -\leftskip + #1\nobreak\hfil \nobreak\hb@xt@\@pnumwidth{\hss #2}\par + \endgroup + \fi} +\newcommand*\l@subsection{\@dottedtocline{2}{1.5em}{2.3em}} +\newcommand*\l@subsubsection{\@dottedtocline{3}{3.8em}{3.2em}} +\newcommand*\l@paragraph{\@dottedtocline{4}{7.0em}{4.1em}} +\newcommand*\l@subparagraph{\@dottedtocline{5}{10em}{5em}} +\newcommand\listoffigures{% + \section*{\listfigurename + \@mkboth{\MakeUppercase\listfigurename}% + {\MakeUppercase\listfigurename}}% + \@starttoc{lof}% + } +\newcommand*\l@figure{\@dottedtocline{1}{1.5em}{2.3em}} +\newcommand\listoftables{% + \section*{\listtablename + \@mkboth{% + \MakeUppercase\listtablename}{\MakeUppercase\listtablename}}% + \@starttoc{lot}% + } +\let\l@table\l@figure +\newdimen\bibindent +\setlength\bibindent{1.5em} +\newenvironment{thebibliography}[1] + {\section*{\refname + \@mkboth{\MakeUppercase\refname}{\MakeUppercase\refname}}% + \list{\@biblabel{\@arabic\c@enumiv}}% + {\settowidth\labelwidth{\@biblabel{#1}}% + \leftmargin\labelwidth + \advance\leftmargin\labelsep + \@openbib@code + \usecounter{enumiv}% + \let\p@enumiv\@empty + \renewcommand\theenumiv{\@arabic\c@enumiv}}% + \sloppy + \clubpenalty4000 + \@clubpenalty \clubpenalty + \widowpenalty4000% + \sfcode`\.\@m} + {\def\@noitemerr + {\@latex@warning{Empty `thebibliography' environment}}% + \endlist} +\newcommand\newblock{\hskip .11em\@plus.33em\@minus.07em} +\let\@openbib@code\@empty +\newenvironment{theindex} + {\if@twocolumn + \@restonecolfalse + \else + \@restonecoltrue + \fi + \columnseprule \z@ + \columnsep 35\p@ + \twocolumn[\section*{\indexname}]% + \@mkboth{\MakeUppercase\indexname}% + {\MakeUppercase\indexname}% + \thispagestyle{plain}\parindent\z@ + \parskip\z@ \@plus .3\p@\relax + \let\item\@idxitem} + {\if@restonecol\onecolumn\else\clearpage\fi} +\newcommand\@idxitem{\par\hangindent 40\p@} +\newcommand\subitem{\@idxitem \hspace*{20\p@}} +\newcommand\subsubitem{\@idxitem \hspace*{30\p@}} +\newcommand\indexspace{\par \vskip 10\p@ \@plus5\p@ \@minus3\p@\relax} +\renewcommand\footnoterule{% + \kern-3\p@ + \hrule\@width.4\columnwidth + \kern2.6\p@} +\newcommand\@makefntext[1]{% + \parindent 1em% + \noindent + \hb@xt@1.8em{\hss\@makefnmark}#1} +\newcommand\contentsname{Contents} +\newcommand\listfigurename{List of Figures} +\newcommand\listtablename{List of Tables} +\newcommand\refname{References} +\newcommand\indexname{Index} +\newcommand\figurename{\small Figure} +\newcommand\tablename{Table} +\newcommand\partname{Part} +\newcommand\appendixname{Appendix} +\newcommand\abstractname{Abstract} +\def\today{\ifcase\month\or + January\or February\or March\or April\or May\or June\or + July\or August\or September\or October\or November\or December\fi + \space\number\day, \number\year} +\setlength\columnsep{10\p@} +\setlength\columnseprule{0\p@} +\pagestyle{plain} +\pagenumbering{arabic} +\if@twoside +\else + \raggedbottom +\fi +\if@twocolumn + \twocolumn + \sloppy + \flushbottom +\else + \onecolumn +\fi +\endinput +%% +%% End of file `article.cls'. diff --git a/conclusion.tex b/conclusion.tex new file mode 100644 index 0000000..f0522c7 --- /dev/null +++ b/conclusion.tex @@ -0,0 +1,17 @@ +Before this work, the second class of +chaos-based PRNG $\textit{CIPRNG}_f^2$ was robust against +batteries of statistical tests and was abusively said to be chaotic. +This work has formally established the proof that +the $\textit{CIPRNG}_f^2$ is chaotic according to the Devaney +definition for some well-chosen functions $f$. +The chaos condition is expressed as a necessary and sufficient condition +on a graph of iterations: this one has to be strongly connected. + +It has thus bridged the gap between the need of true chaos for some +applications and the practical efficiency. +In a future work, we plan to study sufficient conditions on $f$ to +observe this +connectivity +and to study computed functions in the perspective +of mixing time to improve their practical efficiency. + diff --git a/crCOUCHOT14/Example.tex b/crCOUCHOT14/Example.tex new file mode 100644 index 0000000..fac226f --- /dev/null +++ b/crCOUCHOT14/Example.tex @@ -0,0 +1,362 @@ +\documentclass[a4paper,twoside]{article} + +\usepackage{epsfig} +\usepackage{subfigure} +\usepackage{calc} +\usepackage{amssymb} +\usepackage{amstext} +\usepackage{amsmath} +\usepackage{amsthm} +\usepackage{multicol} +\usepackage{pslatex} +\usepackage{apalike} +\usepackage{SCITEPRESS} +\usepackage[small]{caption} + +\subfigtopskip=0pt +\subfigcapskip=0pt +\subfigbottomskip=0pt + +\begin{document} + +\title{Authors' Instructions \subtitle{Preparation of Camera-Ready Contributions to SCITEPRESS Proceedings} } + +\author{\authorname{First Author Name\sup{1}, Second Author Name\sup{1} and Third Author Name\sup{2}} +\affiliation{\sup{1}Institute of Problem Solving, XYZ University, My Street, MyTown, MyCountry} +\affiliation{\sup{2}Department of Computing, Main University, MySecondTown, MyCountry} +\email{\{f\_author, s\_author\}@ips.xyz.edu, t\_author@dc.mu.edu} +} + +\keywords{The paper must have at least one keyword. The text must be set to 9-point font size and without the use of bold or italic font style. For more than one keyword, please use a comma as a separator. Keywords must be titlecased.} + +\abstract{The abstract should summarize the contents of the paper and should contain at least 70 and at most 200 words. The text must be set to 9-point font size.} + +\onecolumn \maketitle \normalsize \vfill + +\section{\uppercase{Introduction}} +\label{sec:introduction} + +\noindent Your paper will be part of the conference proceedings +therefore we ask that authors follow the guidelines explained in +this example in order to achieve the highest quality possible +\cite{Smith98}. + +Be advised that papers in a technically unsuitable form will be +returned for retyping. After returned the manuscript must be +appropriately modified. + +\section{\uppercase{Manuscript Preparation}} + +\noindent We strongly encourage authors to use this document for the +preparation of the camera-ready. Please follow the instructions +closely in order to make the volume look as uniform as possible +\cite{Moore99}. + +Please remember that all the papers must be in English and without +orthographic errors. + +Do not add any text to the headers (do not set running heads) and +footers, not even page numbers, because text will be added +electronically. + +For a best viewing experience the used font must be Times New +Roman, except on special occasions, such as program code +\ref{subsubsec:program_code}. + + +\subsection{Manuscript Setup} + +\noindent The template is composed by a set of 7 files, in the +following 2 groups:\\ +\noindent {\bf Group 1.} To format your paper you will need to copy +into your working directory, but NOT edit, the following 4 files: +\begin{verbatim} + - apalike.bst + - apalike.sty + - article.cls + - scitepress.sty +\end{verbatim} + +\noindent {\bf Group 2.} Additionally, you may wish to copy and edit +the following 3 example files: +\begin{verbatim} + - example.bib + - example.tex + - scitepress.eps +\end{verbatim} + + +\subsection{Page Setup} + +The paper size must be set to A4 (210x297 mm). The document +margins must be the following: + +\begin{itemize} + \item Top: 3,3 cm; + \item Bottom: 4,2 cm; + \item Left: 2,6 cm; + \item Right: 2,6 cm. +\end{itemize} + +It is advisable to keep all the given values because any text or +material outside the aforementioned margins will not be printed. + +\subsection{First Section} + +This section must be in one column. + +\vfill +\subsubsection{Title and Subtitle} + +Use the command \textit{$\backslash$title} and follow the given structure in "example.tex". The title and subtitle must be with initial letters +capitalized (titlecased). If no subtitle is required, please remove the corresponding \textit{$\backslash$subtitle} command. In the title or subtitle, words like "is", "or", "then", etc. should not be capitalized unless they are the first word of the subtitle. No formulas or special characters of any form or language are allowed in the title or subtitle. + +\subsubsection{Authors and Affiliations} + +Use the command \textit{$\backslash$author} and follow the given structure in "example.tex". + +\subsubsection{Keywords} + +Use the command \textit{$\backslash$keywords} and follow the given structure in "example.tex". Each paper must have at least one keyword. If more than one is specified, please use a comma as a separator. The sentence must end with a period. + +\subsubsection{Abstract} + +Use the command \textit{$\backslash$abstract} and follow the given structure in "example.tex". +Each paper must have an abstract up to 200 words. The sentence +must end with a period. + +\subsection{Second Section} + +Files "example.tex" and "example.bib" show how to create a paper +with a corresponding list of references. + +This section must be in two columns. + +Each column must be 7,5-centimeter wide with a column spacing +of 0,8-centimeter. + +The section text must be set to 10-point. + +Section, subsection and sub-subsection first paragraph should not +have the first line indent. + +To remove the paragraph indentation (only necessary for the +sections), use the command \textit{$\backslash$noindent} before the +paragraph first word. + +If you use other style files (.sty) you MUST include them in the +final manuscript zip file. + +\subsubsection{Section Titles} + +The heading of a section title should be in all-capitals. + +Example: \textit{$\backslash$section\{FIRST TITLE\}} + +\vfill +\subsubsection{Subsection Titles} + +The heading of a subsection title must be with initial letters +capitalized (titlecased). + +Words like "is", "or", "then", etc. should not be capitalized unless +they are the first word of the subsection title. + +Example: \textit{$\backslash$subsection\{First Subtitle\}} + +\subsubsection{Sub-Subsection Titles} + +The heading of a sub subsection title should be with initial letters +capitalized (titlecased). + +Words like "is", "or", "then", etc should not be capitalized unless +they are the first word of the sub subsection title. + +Example: \textit{$\backslash$subsubsection\{First Subsubtitle\}} + +\subsubsection{Tables} + +Tables must appear inside the designated margins or they may span +the two columns. + +Tables in two columns must be positioned at the top or bottom of the +page within the given margins. To span a table in two columns please add an asterisk (*) to the table \textit{begin} and \textit{end} command. + +Example: \textit{$\backslash$begin\{table*\}} + +\hspace*{1.5cm}\textit{$\backslash$end\{table*\}}\\ + +Tables should be centered and should always have a caption +positioned above it. The font size to use is 9-point. No bold or +italic font style should be used. + +The final sentence of a caption should end with a period. + +\begin{table}[h] +\caption{This caption has one line so it is +centered.}\label{tab:example1} \centering +\begin{tabular}{|c|c|} + \hline + Example column 1 & Example column 2 \\ + \hline + Example text 1 & Example text 2 \\ + \hline +\end{tabular} +\end{table} + +\begin{table}[h] +\caption{This caption has more than one line so it has to be +justified.}\label{tab:example2} \centering +\begin{tabular}{|c|c|} + \hline + Example column 1 & Example column 2 \\ + \hline + Example text 1 & Example text 2 \\ + \hline +\end{tabular} +\end{table} + +Please note that the word "Table" is spelled out. + + +\subsubsection{Figures} + +Please produce your figures electronically, and integrate them into +your document and zip file. + +Check that in line drawings, lines are not interrupted and have a +constant width. Grids and details within the figures must be clearly +readable and may not be written one on top of the other. + +Figure resolution should be at least 300 dpi. + +Figures must appear inside the designated margins or they may span +the two columns. + +Figures in two columns must be positioned at the top or bottom of +the page within the given margins. To span a figure in two columns please add an asterisk (*) to the figure \textit{begin} and \textit{end} command. + +Example: \textit{$\backslash$begin\{figure*\}} + +\hspace*{1.5cm}\textit{$\backslash$end\{figure*\}} + +Figures should be centered and should always have a caption +positioned under it. The font size to use is 9-point. No bold or +italic font style should be used. + +\begin{figure}[!h] + %\vspace{-0.2cm} + \centering + {\epsfig{file = SCITEPRESS.eps, width = 5.5cm}} + \caption{This caption has one line so it is centered.} + \label{fig:example1} + \end{figure} + +\begin{figure}[!h] + \vspace{-0.2cm} + \centering + {\epsfig{file = SCITEPRESS.eps, width = 5.5cm}} + \caption{This caption has more than one line so it has to be justified.} + \label{fig:example2} + \vspace{-0.1cm} +\end{figure} + +The final sentence of a caption should end with a period. + + + +Please note that the word "Figure" is spelled out. + +\subsubsection{Equations} + +Equations should be placed on a separate line, numbered and +centered.\\The numbers accorded to equations should appear in +consecutive order inside each section or within the contribution, +with the number enclosed in brackets and justified to the right, +starting with the number 1. + +Example: + +\begin{equation}\label{eq1} + a=b+c +\end{equation} + +\subsubsection{Program Code}\label{subsubsec:program_code} + +Program listing or program commands in text should be set in +typewriter form such as Courier New. + +Example of a Computer Program in Pascal: + +\begin{small} +\begin{verbatim} + Begin + Writeln('Hello World!!'); + End. +\end{verbatim} +\end{small} + + +The text must be aligned to the left and in 9-point type. + +\vfill +\subsubsection{Reference Text and Citations} + +References and citations should follow the Harvard (Author, date) +System Convention (see the References section in the compiled +manuscript). As example you may consider the citation +\cite{Smith98}. Besides that, all references should be cited in the +text. No numbers with or without brackets should be used to list the +references. + +References should be set to 9-point. Citations should be 10-point +font size. + +You may check the structure of "example.bib" before constructing the +references. + +For more instructions about the references and citations usage +please see the appropriate link at the conference website. + +\section{\uppercase{Copyright Form}} + +\noindent For the mutual benefit and protection of Authors and +Publishers, it is necessary that Authors provide formal written +Consent to Publish and Transfer of Copyright before publication of +the Book. The signed Consent ensures that the publisher has the +Author's authorization to publish the Contribution. + +The copyright form is located on the authors' reserved area. + +The printed form should be completed and signed by one author on +behalf of all the other authors, and uploaded through the authors' reserved area. Alternatively, you can send it to the secretariat by e-mail or fax. + +\section{\uppercase{Conclusions}} +\label{sec:conclusion} + +\noindent Please note that ONLY the files required to compile your paper should be submitted. Previous versions or examples MUST be removed from the compilation directory before submission. + +We hope you find the information in this template useful in the preparation of your submission. + +\section*{\uppercase{Acknowledgements}} + +\noindent If any, should be placed before the references section +without numbering. To do so please use the following command: +\textit{$\backslash$section*\{ACKNOWLEDGEMENTS\}} + + +\vfill +\bibliographystyle{apalike} +{\small +\bibliography{example}} + + +\section*{\uppercase{Appendix}} + +\noindent If any, the appendix should appear directly after the +references without numbering, and not on a new page. To do so please use the following command: +\textit{$\backslash$section*\{APPENDIX\}} + +\vfill +\end{document} + diff --git a/crCOUCHOT14/SCITEPRESS.eps b/crCOUCHOT14/SCITEPRESS.eps new file mode 100644 index 0000000..45e720a Binary files /dev/null and b/crCOUCHOT14/SCITEPRESS.eps differ diff --git a/crCOUCHOT14/SCITEPRESS.sty b/crCOUCHOT14/SCITEPRESS.sty new file mode 100644 index 0000000..8b5b5be --- /dev/null +++ b/crCOUCHOT14/SCITEPRESS.sty @@ -0,0 +1,162 @@ +\typeout{Conference Style for SCITEPRESS for LaTeX 2e -- version of April 2013} + +\pagestyle{empty} +\setlength\paperheight{297mm} +\setlength\paperwidth{210mm} + + +\setlength\topmargin{-0.91in} \setlength\oddsidemargin{0.02362in} +\setlength\evensidemargin{0.02362in} + +\setlength\textheight{8.74in} \setlength\textwidth{6.221in} +\setlength\columnsep{0.8cm} +\newlength\titlebox %\setlength\titlebox{2in} +\setlength\headheight{0pt} \setlength\headsep{36pt} +\thispagestyle{empty} \pagestyle{empty} + +\flushbottom \twocolumn \sloppy + +\def\addcontentsline#1#2#3{} + + + +%%First Section +\def\title#1{\gdef\@title{ #1 \\[15pt]{\textmd {\textbf }}\\}} +\newcommand{\subtitle}[1]{\\ \fontsize{13}{15}\selectfont \textit{#1 } } + +\def\keywords#1{\gdef\@keywords{\small Keywords: \hspace{0.388cm} \begin{minipage}[t]{5.45in} \fontsize{9}{11}\selectfont \vspace{-0.22cm} #1 \\ \end{minipage}}} +%\gdef\@mykeywords{} +\def\abstract#1{\gdef\@abstract{\ \\ \small Abstract: \hspace{0.6cm} \begin{minipage}[t]{5.45in} \fontsize{9}{11}\selectfont \vspace{-0.22cm} #1 \end{minipage} }} + +%%%%%%% +\def\sup#1{$^{#1}$} + +\newcommand{\authorname}[1]{\fontsize{11}{13}\selectfont #1 \\ }%\addtocounter{authorcounter}{1}} +\newcommand{\affiliation}[1]{\begin{minipage}[t]{6.2in} \centering \fontsize{9}{11}\selectfont \textit{ #1} \end{minipage} \\} +\newcommand{\email}[1]{\fontsize{9}{11}\selectfont \textit{#1} \\[12pt]} + + +%%%%%%% +\def\maketitle{\par +\begingroup +% to make the footnote style local to the title +\def\thefootnote{\fnsymbol{footnote}} +\twocolumn[ + +\centering {\LARGE\bf \@title \par} +\vskip -0.07in + +\centering\@author +\vskip 0.51in + +\@keywords +\vskip 0.02in + +\@abstract + +\vspace{32pt} + +] + + +\@thanks +\endgroup + +\let\maketitle\relax \let\@maketitle\relax +\gdef\@thanks{}\gdef\@author{}\gdef\@title{}\let\thanks\relax} + + + +%%Paper Contents and References + +\def\pubnote#1{\thispagestyle{myheadings} +\pagestyle{myheadings} +\markboth{#1}{#1} +\setlength\headheight{10pt} \setlength\headsep{10pt} +} + +% sections with less space +\def\section{\@startsection{section}{1}{\z@}{24pt plus 2pt minus 1pt} +{12pt plus 2pt minus 1pt}{\Large\bf\raggedright}} +\def\subsection{\@startsection{subsection}{2}{\z@}{-2.0ex plus +-0.5ex minus -.2ex}{12pt plus 2pt minus 1pt}{\large\bf\raggedright}} +\def\subsubsection{\@startsection{subsubsection}{3}{\z@}{-2.0ex plus +-0.5ex minus -.2ex}{12pt plus 2pt minus 1pt}{\normalsize\bf\raggedright}} + + +% Footnotes +\footnotesep 6.65pt % +\skip\footins 9pt plus 4pt minus 2pt +\def\footnoterule{\kern-3pt \hrule width 5pc \kern 2.6pt } + +% Lists and paragraphs +\parindent 0.5cm +\topsep 4pt plus 1pt minus 2pt +\partopsep 1pt plus 0.5pt minus 0.5pt +\itemsep 2pt plus 1pt minus 0.5pt +\parsep 2pt plus 1pt minus 0.5pt +\leftmargin 15pt \leftmargini\leftmargin \leftmarginii 10pt +\leftmarginiii 5pt \leftmarginiv 5pt \leftmarginv 5pt \leftmarginvi +5pt \labelwidth\leftmargini\advance\labelwidth-\labelsep \labelsep +5pt +\def\@listi{\leftmargin\leftmargini} +\def\@listii{\leftmargin\leftmarginii +\labelwidth\leftmarginii\advance\labelwidth-\labelsep +\topsep 2pt plus 1pt minus 0.5pt +\parsep 1pt plus 0.5pt minus 0.5pt +\itemsep \parsep} +\def\@listiii{\leftmargin\leftmarginiii +\labelwidth\leftmarginiii\advance\labelwidth-\labelsep +\topsep 1pt plus 0.5pt minus 0.5pt +\parsep \z@ \partopsep 0.5pt plus 0pt minus 0.5pt +\itemsep \topsep} +\def\@listiv{\leftmargin\leftmarginiv +\labelwidth\leftmarginiv\advance\labelwidth-\labelsep} +\def\@listv{\leftmargin\leftmarginv +\labelwidth\leftmarginv\advance\labelwidth-\labelsep} +\def\@listvi{\leftmargin\leftmarginvi +\labelwidth\leftmarginvi\advance\labelwidth-\labelsep} +\abovedisplayskip 7pt plus2pt minus5pt% +\belowdisplayskip \abovedisplayskip +\abovedisplayshortskip 0pt plus3pt% +\belowdisplayshortskip 4pt plus3pt minus3pt% + +%%%%%% +\setlength{\abovecaptionskip}{4pt}%plus3pt minus3pt}% +\setlength{\belowcaptionskip}{-4pt}%plus3pt minus3pt} +%%%%%% +% Less leading in most fonts (due to the narrow columns) +% The choices were between 1-pt and 1.5-pt leading +\def\normalsize{\@setfontsize\normalsize\@xpt{11}} % 10 point on 11 +\def\small{\@setfontsize\small\@ixpt{10}} % 9 point on 10 +\def\smalll{\@setfontsize\smalll\@viiipt{10}} % 9 point on 9 +\def\footnotesize{\@setfontsize\footnotesize\@ixpt{10}} % 9 point on 10 +\def\scriptsize{\@setfontsize\scriptsize\@viipt{10}} % 7 point on 8 +\def\tiny{\@setfontsize\tiny\@vipt{7}} % 6 point on 7 +\def\large{\@setfontsize\large\@xipt{12}} % 11 point on 12 +\def\Large{\@setfontsize\Large\@xiipt{14}} % 12 point on 14 +\def\LARGE{\@setfontsize\LARGE\@xivpt{16}} % 14 point on 16 +\def\huge{\@setfontsize\huge\@xviipt{20}} % 17 point on 20 +\def\Huge{\@setfontsize\Huge\@xxpt{23}} % 20 point on 23 + +\setlength{\topmargin}{-1.1cm} \addtolength{\textheight}{-0.1cm} +\setlength{\headsep}{1.9cm} +\setlength{\footskip}{1.7cm} + +\renewcommand{\large}{\fontsize{12}{15}\selectfont} +\renewcommand{\Large}{\fontsize{13}{15}\selectfont} +\renewcommand{\normalsize}{\fontsize{10}{11.5}\selectfont} +\renewcommand{\refname}{REFERENCES} + +\newcommand{\F}{\mathcal{F}} +\newcommand{\I}{\mathcal{I}} +\newcommand{\D}{\mathcal{D}} +\newcommand{\T}{\mathcal{T}} +\newcommand{\R}{\mathcal{R}} +\newcommand{\rr}{\mathfrak{r}} +\newcommand{\code}[1]{\textsf{#1}} + +\renewcommand\floatpagefraction{.9} +\renewcommand\topfraction{.9} +\renewcommand\bottomfraction{.9} +\renewcommand\textfraction{.1} \ No newline at end of file diff --git a/crCOUCHOT14/abstract.tex b/crCOUCHOT14/abstract.tex new file mode 100644 index 0000000..6fbefec --- /dev/null +++ b/crCOUCHOT14/abstract.tex @@ -0,0 +1,17 @@ +Chaotic functions are often successfully embedded +into pseudorandom sequence generators. +However even if these generators +can effectively face statistical tests +(thanks to optimized parameters), they may lose +their chaos properties since +they are designed using floating point numbers instead of real ones +numbers. +In a previous work, we had constructed chaos-based PRNGs +defined on a discrete domain. In this context, proofs that are +formally established are preserved during the execution. +We had shown that these generators successfully pass +the most stringent statistical tests +and we had proven that some of them are chaotic. +This work completes this task and shows that +this whole class of PRNGS is chaotic +if and only if some given graphs of iteration are strongly connected. diff --git a/crCOUCHOT14/apalike.bst b/crCOUCHOT14/apalike.bst new file mode 100644 index 0000000..a7d00ff --- /dev/null +++ b/crCOUCHOT14/apalike.bst @@ -0,0 +1,1102 @@ +%NAME: apalike.bst +% BibTeX `apalike' bibliography style (24-Jan-88 version) +% Adapted from the `alpha' style, version 0.99a; for BibTeX version 0.99a. +% Copyright (C) 1988, all rights reserved. +% Copying of this file is allowed, provided that if you make any changes at all +% you name it something other than `apalike.bst'. +% This restriction helps ensure that all copies are identical. +% Differences between this style and `alpha' are generally heralded by a `%'. +% The file btxbst.doc has the documentation for alpha.bst. +% +% This style should be used with the `apalike' LaTeX style (apalike.sty). +% \cite's come out like "(Jones, 1986)" in the text but there are no labels +% in the bibliography, and something like "(1986)" comes out immediately +% after the author. Author (and editor) names appear as last name, comma, +% initials. A `year' field is required for every entry, and so is either +% an author (or in some cases, an editor) field or a key field. +% +% Editorial note: +% Many journals require a style like `apalike', but I strongly, strongly, +% strongly recommend that you not use it if you have a choice---use something +% like `plain' instead. Mary-Claire van Leunen (A Handbook for Scholars, +% Knopf, 1979) argues convincingly that a style like `plain' encourages better +% writing than one like `apalike'. Furthermore the strongest arguments for +% using an author-date style like `apalike'---that it's "the most practical" +% (The Chicago Manual of Style, University of Chicago Press, thirteenth +% edition, 1982, pages 400--401)---fall flat on their face with the new +% computer-typesetting technology. For instance page 401 anachronistically +% states "The chief disadvantage of [a style like `plain'] is that additions +% or deletions cannot be made after the manuscript is typed without changing +% numbers in both text references and list." LaTeX sidesteps the disadvantage. +% +% History: +% 15-sep-86 (SK,OP) Original version, by Susan King and Oren Patashnik. +% 10-nov-86 (OP) Truncated the sort.key$ string to the correct length +% in bib.sort.order to eliminate error message. +% 24-jan-88 (OP) Updated for BibTeX version 0.99a, from alpha.bst 0.99a; +% apalike now sorts by author, then year, then title; +% THIS `apalike' VERSION DOES NOT WORK WITH BIBTEX 0.98i. + +ENTRY + { address + author + booktitle + chapter + edition + editor + howpublished + institution + journal + key +% month not used in apalike + note + number + organization + pages + publisher + school + series + title + type + volume + year + } + {} + { label extra.label sort.label } + +INTEGERS { output.state before.all mid.sentence after.sentence after.block } + +FUNCTION {init.state.consts} +{ #0 'before.all := + #1 'mid.sentence := + #2 'after.sentence := + #3 'after.block := +} + +STRINGS { s t } + +FUNCTION {output.nonnull} +{ 's := + output.state mid.sentence = + { ", " * write$ } + { output.state after.block = + { add.period$ write$ + newline$ + "\newblock " write$ + } + { output.state before.all = + 'write$ + { add.period$ " " * write$ } + if$ + } + if$ + mid.sentence 'output.state := + } + if$ + s +} + +FUNCTION {output} +{ duplicate$ empty$ + 'pop$ + 'output.nonnull + if$ +} + +FUNCTION {output.check} +{ 't := + duplicate$ empty$ + { pop$ "empty " t * " in " * cite$ * warning$ } + 'output.nonnull + if$ +} + +% apalike needs this function because +% the year has special punctuation; +% apalike ignores the month +FUNCTION {output.year.check} +{ year empty$ + { "empty year in " cite$ * warning$ } + { write$ + " (" year * extra.label * ")" * + mid.sentence 'output.state := + } + if$ +} + +FUNCTION {output.bibitem} +{ newline$ + "\bibitem[" write$ + label write$ + "]{" write$ + cite$ write$ + "}" write$ + newline$ + "" + before.all 'output.state := +} + +FUNCTION {fin.entry} +{ add.period$ + write$ + newline$ +} + +FUNCTION {new.block} +{ output.state before.all = + 'skip$ + { after.block 'output.state := } + if$ +} + +FUNCTION {new.sentence} +{ output.state after.block = + 'skip$ + { output.state before.all = + 'skip$ + { after.sentence 'output.state := } + if$ + } + if$ +} + +FUNCTION {not} +{ { #0 } + { #1 } + if$ +} + +FUNCTION {and} +{ 'skip$ + { pop$ #0 } + if$ +} + +FUNCTION {or} +{ { pop$ #1 } + 'skip$ + if$ +} + +FUNCTION {new.block.checkb} +{ empty$ + swap$ empty$ + and + 'skip$ + 'new.block + if$ +} + +FUNCTION {field.or.null} +{ duplicate$ empty$ + { pop$ "" } + 'skip$ + if$ +} + +FUNCTION {emphasize} +{ duplicate$ empty$ + { pop$ "" } + { "{\em " swap$ * "}" * } + if$ +} + +INTEGERS { nameptr namesleft numnames } + +FUNCTION {format.names} +{ 's := + #1 'nameptr := + s num.names$ 'numnames := + numnames 'namesleft := + { namesleft #0 > } + { s nameptr "{vv~}{ll}{, jj}{, f.}" format.name$ 't := % last name first + nameptr #1 > + { namesleft #1 > + { ", " * t * } + { numnames #2 > + { "," * } + 'skip$ + if$ + t "others" = + { " et~al." * } + { " and " * t * } + if$ + } + if$ + } + 't + if$ + nameptr #1 + 'nameptr := + namesleft #1 - 'namesleft := + } + while$ +} + +FUNCTION {format.authors} +{ author empty$ + { "" } + { author format.names } + if$ +} + +FUNCTION {format.key} % this function is just for apalike +{ empty$ + { key field.or.null } + { "" } + if$ +} + +FUNCTION {format.editors} +{ editor empty$ + { "" } + { editor format.names + editor num.names$ #1 > + { ", editors" * } + { ", editor" * } + if$ + } + if$ +} + +FUNCTION {format.title} +{ title empty$ + { "" } + { title "t" change.case$ } + if$ +} + +FUNCTION {n.dashify} +{ 't := + "" + { t empty$ not } + { t #1 #1 substring$ "-" = + { t #1 #2 substring$ "--" = not + { "--" * + t #2 global.max$ substring$ 't := + } + { { t #1 #1 substring$ "-" = } + { "-" * + t #2 global.max$ substring$ 't := + } + while$ + } + if$ + } + { t #1 #1 substring$ * + t #2 global.max$ substring$ 't := + } + if$ + } + while$ +} + +FUNCTION {format.btitle} +{ title emphasize +} + +FUNCTION {tie.or.space.connect} +{ duplicate$ text.length$ #3 < + { "~" } + { " " } + if$ + swap$ * * +} + +FUNCTION {either.or.check} +{ empty$ + 'pop$ + { "can't use both " swap$ * " fields in " * cite$ * warning$ } + if$ +} + +FUNCTION {format.bvolume} +{ volume empty$ + { "" } + { "volume" volume tie.or.space.connect + series empty$ + 'skip$ + { " of " * series emphasize * } + if$ + "volume and number" number either.or.check + } + if$ +} + +FUNCTION {format.number.series} +{ volume empty$ + { number empty$ + { series field.or.null } + { output.state mid.sentence = + { "number" } + { "Number" } + if$ + number tie.or.space.connect + series empty$ + { "there's a number but no series in " cite$ * warning$ } + { " in " * series * } + if$ + } + if$ + } + { "" } + if$ +} + +FUNCTION {format.edition} +{ edition empty$ + { "" } + { output.state mid.sentence = + { edition "l" change.case$ " edition" * } + { edition "t" change.case$ " edition" * } + if$ + } + if$ +} + +INTEGERS { multiresult } + +FUNCTION {multi.page.check} +{ 't := + #0 'multiresult := + { multiresult not + t empty$ not + and + } + { t #1 #1 substring$ + duplicate$ "-" = + swap$ duplicate$ "," = + swap$ "+" = + or or + { #1 'multiresult := } + { t #2 global.max$ substring$ 't := } + if$ + } + while$ + multiresult +} + +FUNCTION {format.pages} +{ pages empty$ + { "" } + { pages multi.page.check + { "pages" pages n.dashify tie.or.space.connect } + { "page" pages tie.or.space.connect } + if$ + } + if$ +} + +FUNCTION {format.vol.num.pages} +{ volume field.or.null + number empty$ + 'skip$ + { "(" number * ")" * * + volume empty$ + { "there's a number but no volume in " cite$ * warning$ } + 'skip$ + if$ + } + if$ + pages empty$ + 'skip$ + { duplicate$ empty$ + { pop$ format.pages } + { ":" * pages n.dashify * } + if$ + } + if$ +} + +FUNCTION {format.chapter.pages} +{ chapter empty$ + 'format.pages + { type empty$ + { "chapter" } + { type "l" change.case$ } + if$ + chapter tie.or.space.connect + pages empty$ + 'skip$ + { ", " * format.pages * } + if$ + } + if$ +} + +FUNCTION {format.in.ed.booktitle} +{ booktitle empty$ + { "" } + { editor empty$ + { "In " booktitle emphasize * } + { "In " format.editors * ", " * booktitle emphasize * } + if$ + } + if$ +} + +FUNCTION {format.thesis.type} +{ type empty$ + 'skip$ + { pop$ + type "t" change.case$ + } + if$ +} + +FUNCTION {format.tr.number} +{ type empty$ + { "Technical Report" } + 'type + if$ + number empty$ + { "t" change.case$ } + { number tie.or.space.connect } + if$ +} + +FUNCTION {format.article.crossref} +{ "In" % this is for apalike + " \cite{" * crossref * "}" * +} + +FUNCTION {format.book.crossref} +{ volume empty$ + { "empty volume in " cite$ * "'s crossref of " * crossref * warning$ + "In " + } + { "Volume" volume tie.or.space.connect + " of " * + } + if$ + "\cite{" * crossref * "}" * % this is for apalike +} + +FUNCTION {format.incoll.inproc.crossref} +{ "In" % this is for apalike + " \cite{" * crossref * "}" * +} + +FUNCTION {article} +{ output.bibitem + format.authors "author" output.check + author format.key output % special for + output.year.check % apalike + new.block + format.title "title" output.check + new.block + crossref missing$ + { journal emphasize "journal" output.check + format.vol.num.pages output + } + { format.article.crossref output.nonnull + format.pages output + } + if$ + new.block + note output + fin.entry +} + +FUNCTION {book} +{ output.bibitem + author empty$ + { format.editors "author and editor" output.check + editor format.key output + } + { format.authors output.nonnull + crossref missing$ + { "author and editor" editor either.or.check } + 'skip$ + if$ + } + if$ + output.year.check % special for apalike + new.block + format.btitle "title" output.check + crossref missing$ + { format.bvolume output + new.block + format.number.series output + new.sentence + publisher "publisher" output.check + address output + } + { new.block + format.book.crossref output.nonnull + } + if$ + format.edition output + new.block + note output + fin.entry +} + +FUNCTION {booklet} +{ output.bibitem + format.authors output + author format.key output % special for + output.year.check % apalike + new.block + format.title "title" output.check + new.block + howpublished output + address output + new.block + note output + fin.entry +} + +FUNCTION {inbook} +{ output.bibitem + author empty$ + { format.editors "author and editor" output.check + editor format.key output + } + { format.authors output.nonnull + crossref missing$ + { "author and editor" editor either.or.check } + 'skip$ + if$ + } + if$ + output.year.check % special for apalike + new.block + format.btitle "title" output.check + crossref missing$ + { format.bvolume output + format.chapter.pages "chapter and pages" output.check + new.block + format.number.series output + new.sentence + publisher "publisher" output.check + address output + } + { format.chapter.pages "chapter and pages" output.check + new.block + format.book.crossref output.nonnull + } + if$ + format.edition output + new.block + note output + fin.entry +} + +FUNCTION {incollection} +{ output.bibitem + format.authors "author" output.check + author format.key output % special for + output.year.check % apalike + new.block + format.title "title" output.check + new.block + crossref missing$ + { format.in.ed.booktitle "booktitle" output.check + format.bvolume output + format.number.series output + format.chapter.pages output + new.sentence + publisher "publisher" output.check + address output + format.edition output + } + { format.incoll.inproc.crossref output.nonnull + format.chapter.pages output + } + if$ + new.block + note output + fin.entry +} + +FUNCTION {inproceedings} +{ output.bibitem + format.authors "author" output.check + author format.key output % special for + output.year.check % apalike + new.block + format.title "title" output.check + new.block + crossref missing$ + { format.in.ed.booktitle "booktitle" output.check + format.bvolume output + format.number.series output + format.pages output + address output % for apalike + new.sentence % there's no year + organization output % here so things + publisher output % are simpler + } + { format.incoll.inproc.crossref output.nonnull + format.pages output + } + if$ + new.block + note output + fin.entry +} + +FUNCTION {conference} { inproceedings } + +FUNCTION {manual} +{ output.bibitem + format.authors output + author format.key output % special for + output.year.check % apalike + new.block + format.btitle "title" output.check + organization address new.block.checkb + organization output + address output + format.edition output + new.block + note output + fin.entry +} + +FUNCTION {mastersthesis} +{ output.bibitem + format.authors "author" output.check + author format.key output % special for + output.year.check % apalike + new.block + format.title "title" output.check + new.block + "Master's thesis" format.thesis.type output.nonnull + school "school" output.check + address output + new.block + note output + fin.entry +} + +FUNCTION {misc} +{ output.bibitem + format.authors output + author format.key output % special for + output.year.check % apalike + new.block + format.title output + new.block + howpublished output + new.block + note output + fin.entry +} + +FUNCTION {phdthesis} +{ output.bibitem + format.authors "author" output.check + author format.key output % special for + output.year.check % apalike + new.block + format.btitle "title" output.check + new.block + "PhD thesis" format.thesis.type output.nonnull + school "school" output.check + address output + new.block + note output + fin.entry +} + +FUNCTION {proceedings} +{ output.bibitem + format.editors output + editor format.key output % special for + output.year.check % apalike + new.block + format.btitle "title" output.check + format.bvolume output + format.number.series output + address output % for apalike + new.sentence % we always output + organization output % a nonempty organization + publisher output % here + new.block + note output + fin.entry +} + +FUNCTION {techreport} +{ output.bibitem + format.authors "author" output.check + author format.key output % special for + output.year.check % apalike + new.block + format.title "title" output.check + new.block + format.tr.number output.nonnull + institution "institution" output.check + address output + new.block + note output + fin.entry +} + +FUNCTION {unpublished} +{ output.bibitem + format.authors "author" output.check + author format.key output % special for + output.year.check % apalike + new.block + format.title "title" output.check + new.block + note "note" output.check + fin.entry +} + +FUNCTION {default.type} { misc } + +MACRO {jan} {"January"} + +MACRO {feb} {"February"} + +MACRO {mar} {"March"} + +MACRO {apr} {"April"} + +MACRO {may} {"May"} + +MACRO {jun} {"June"} + +MACRO {jul} {"July"} + +MACRO {aug} {"August"} + +MACRO {sep} {"September"} + +MACRO {oct} {"October"} + +MACRO {nov} {"November"} + +MACRO {dec} {"December"} + +MACRO {acmcs} {"ACM Computing Surveys"} + +MACRO {acta} {"Acta Informatica"} + +MACRO {cacm} {"Communications of the ACM"} + +MACRO {ibmjrd} {"IBM Journal of Research and Development"} + +MACRO {ibmsj} {"IBM Systems Journal"} + +MACRO {ieeese} {"IEEE Transactions on Software Engineering"} + +MACRO {ieeetc} {"IEEE Transactions on Computers"} + +MACRO {ieeetcad} + {"IEEE Transactions on Computer-Aided Design of Integrated Circuits"} + +MACRO {ipl} {"Information Processing Letters"} + +MACRO {jacm} {"Journal of the ACM"} + +MACRO {jcss} {"Journal of Computer and System Sciences"} + +MACRO {scp} {"Science of Computer Programming"} + +MACRO {sicomp} {"SIAM Journal on Computing"} + +MACRO {tocs} {"ACM Transactions on Computer Systems"} + +MACRO {tods} {"ACM Transactions on Database Systems"} + +MACRO {tog} {"ACM Transactions on Graphics"} + +MACRO {toms} {"ACM Transactions on Mathematical Software"} + +MACRO {toois} {"ACM Transactions on Office Information Systems"} + +MACRO {toplas} {"ACM Transactions on Programming Languages and Systems"} + +MACRO {tcs} {"Theoretical Computer Science"} + +READ + +FUNCTION {sortify} +{ purify$ + "l" change.case$ +} + +INTEGERS { len } + +FUNCTION {chop.word} +{ 's := + 'len := + s #1 len substring$ = + { s len #1 + global.max$ substring$ } + 's + if$ +} + +% There are three apalike cases: one person (Jones), +% two (Jones and de~Bruijn), and more (Jones et~al.). +% This function is much like format.crossref.editors. +% +FUNCTION {format.lab.names} +{ 's := + s #1 "{vv~}{ll}" format.name$ + s num.names$ duplicate$ + #2 > + { pop$ " et~al." * } + { #2 < + 'skip$ + { s #2 "{ff }{vv }{ll}{ jj}" format.name$ "others" = + { " et~al." * } + { " and " * s #2 "{vv~}{ll}" format.name$ * } + if$ + } + if$ + } + if$ +} + +FUNCTION {author.key.label} +{ author empty$ + { key empty$ + { cite$ #1 #3 substring$ } + 'key % apalike uses the whole key + if$ + } + { author format.lab.names } + if$ +} + +FUNCTION {author.editor.key.label} +{ author empty$ + { editor empty$ + { key empty$ + { cite$ #1 #3 substring$ } + 'key % apalike uses the whole key + if$ + } + { editor format.lab.names } + if$ + } + { author format.lab.names } + if$ +} + +FUNCTION {editor.key.label} +{ editor empty$ + { key empty$ + { cite$ #1 #3 substring$ } + 'key % apalike uses the whole key, no organization + if$ + } + { editor format.lab.names } + if$ +} + +FUNCTION {calc.label} +{ type$ "book" = + type$ "inbook" = + or + 'author.editor.key.label + { type$ "proceedings" = + 'editor.key.label % apalike ignores organization + 'author.key.label % for labeling and sorting + if$ + } + if$ + ", " % these three lines are + * % for apalike, which + year field.or.null purify$ #-1 #4 substring$ % uses all four digits + * + 'label := +} + +FUNCTION {sort.format.names} +{ 's := + #1 'nameptr := + "" + s num.names$ 'numnames := + numnames 'namesleft := + { namesleft #0 > } + { nameptr #1 > + { " " * } + 'skip$ + if$ % apalike uses initials + s nameptr "{vv{ } }{ll{ }}{ f{ }}{ jj{ }}" format.name$ 't := % <= here + nameptr numnames = t "others" = and + { "et al" * } + { t sortify * } + if$ + nameptr #1 + 'nameptr := + namesleft #1 - 'namesleft := + } + while$ +} + +FUNCTION {sort.format.title} +{ 't := + "A " #2 + "An " #3 + "The " #4 t chop.word + chop.word + chop.word + sortify + #1 global.max$ substring$ +} + +FUNCTION {author.sort} +{ author empty$ + { key empty$ + { "to sort, need author or key in " cite$ * warning$ + "" + } + { key sortify } + if$ + } + { author sort.format.names } + if$ +} + +FUNCTION {author.editor.sort} +{ author empty$ + { editor empty$ + { key empty$ + { "to sort, need author, editor, or key in " cite$ * warning$ + "" + } + { key sortify } + if$ + } + { editor sort.format.names } + if$ + } + { author sort.format.names } + if$ +} + +FUNCTION {editor.sort} +{ editor empty$ + { key empty$ + { "to sort, need editor or key in " cite$ * warning$ + "" + } + { key sortify } + if$ + } + { editor sort.format.names } + if$ +} + +% apalike uses two sorting passes; the first one sets the +% labels so that the `a's, `b's, etc. can be computed; +% the second pass puts the references in "correct" order. +% The presort function is for the first pass. It computes +% label, sort.label, and title, and then concatenates. +FUNCTION {presort} +{ calc.label + label sortify + " " + * + type$ "book" = + type$ "inbook" = + or + 'author.editor.sort + { type$ "proceedings" = + 'editor.sort + 'author.sort + if$ + } + if$ + #1 entry.max$ substring$ % for + 'sort.label := % apalike + sort.label % style + * + " " + * + title field.or.null + sort.format.title + * + #1 entry.max$ substring$ + 'sort.key$ := +} + +ITERATE {presort} + +SORT % by label, sort.label, title---for final label calculation + +STRINGS { last.label next.extra } % apalike labels are only for the text; + +INTEGERS { last.extra.num } % there are none in the bibliography + +FUNCTION {initialize.extra.label.stuff} % and hence there is no `longest.label' +{ #0 int.to.chr$ 'last.label := + "" 'next.extra := + #0 'last.extra.num := +} + +FUNCTION {forward.pass} +{ last.label label = + { last.extra.num #1 + 'last.extra.num := + last.extra.num int.to.chr$ 'extra.label := + } + { "a" chr.to.int$ 'last.extra.num := + "" 'extra.label := + label 'last.label := + } + if$ +} + +FUNCTION {reverse.pass} +{ next.extra "b" = + { "a" 'extra.label := } + 'skip$ + if$ + label extra.label * 'label := + extra.label 'next.extra := +} + +EXECUTE {initialize.extra.label.stuff} + +ITERATE {forward.pass} + +REVERSE {reverse.pass} + +% Now that the label is right we sort for real, +% on sort.label then year then title. This is +% for the second sorting pass. +FUNCTION {bib.sort.order} +{ sort.label + " " + * + year field.or.null sortify + * + " " + * + title field.or.null + sort.format.title + * + #1 entry.max$ substring$ + 'sort.key$ := +} + +ITERATE {bib.sort.order} + +SORT % by sort.label, year, title---giving final bibliography order + +FUNCTION {begin.bib} +{ preamble$ empty$ % no \etalchar in apalike + 'skip$ + { preamble$ write$ newline$ } + if$ + "\begin{thebibliography}{}" write$ newline$ % no labels in apalike +} + +EXECUTE {begin.bib} + +EXECUTE {init.state.consts} + +ITERATE {call.type$} + +FUNCTION {end.bib} +{ newline$ + "\end{thebibliography}" write$ newline$ +} + +EXECUTE {end.bib} diff --git a/crCOUCHOT14/apalike.sty b/crCOUCHOT14/apalike.sty new file mode 100644 index 0000000..09863b7 --- /dev/null +++ b/crCOUCHOT14/apalike.sty @@ -0,0 +1,31 @@ +\def\@cite#1#2{(#1\if@tempswa , #2\fi)} +\def\@biblabel#1{} + +\newlength{\bibhang} +\setlength{\bibhang}{2em} + +\@ifundefined{chapter}{\def\thebibliography#1{\section*{REFERENCES\@mkboth + {REFERENCES}{REFERENCES}}\list + {\relax}{\setlength{\labelsep}{0em} + \setlength{\itemindent}{-\bibhang} + \setlength{\leftmargin}{\bibhang}} + \itemsep 0pt\parsep 0pt + \def\newblock{\hskip .11em plus .33em minus .07em} + \sloppy\clubpenalty4000\widowpenalty4000 + \sfcode`\.=1000\relax}}% +{\def\thebibliography#1{\chapter*{Bibliography\@mkboth + {BIBLIOGRAPHY}{BIBLIOGRAPHY}}\list + {\relax}{\setlength{\labelsep}{0em} + \setlength{\itemindent}{-\bibhang} + \setlength{\leftmargin}{\bibhang}} + \itemsep 0pt\parsep 0pt + \def\newblock{\hskip .11em plus .33em minus .07em} + \sloppy\clubpenalty4000\widowpenalty4000 + \sfcode`\.=1000\relax}} + +\def\@citex[#1]#2{\if@filesw\immediate\write\@auxout{\string\citation{#2}}\fi + \def\@citea{}\@cite{\@for\@citeb:=#2\do + {\@citea\def\@citea{; }\@ifundefined + {b@\@citeb}{{\bf ?}\@warning + {Citation `\@citeb' on page \thepage \space undefined}}% +{\csname b@\@citeb\endcsname}}}{#1}} diff --git a/crCOUCHOT14/article.cls b/crCOUCHOT14/article.cls new file mode 100644 index 0000000..512b8a4 --- /dev/null +++ b/crCOUCHOT14/article.cls @@ -0,0 +1,642 @@ +%% +%% This is file `article.cls', +%% generated with the docstrip utility. +%% +%% The original source files were: +%% +%% classes.dtx (with options: `article') +%% +%% This is a generated file. +%% +%% Copyright 1993 1994 1995 1996 1997 1998 1999 2000 +%% The LaTeX3 Project and any individual authors listed elsewhere +%% in this file. +%% +%% This file was generated from file(s) of the LaTeX base system. +%% -------------------------------------------------------------- +%% +%% It may be distributed and/or modified under the +%% conditions of the LaTeX Project Public License, either version 1.2 +%% of this license or (at your option) any later version. +%% The latest version of this license is in +%% http://www.latex-project.org/lppl.txt +%% and version 1.2 or later is part of all distributions of LaTeX +%% version 1999/12/01 or later. +%% +%% This file may only be distributed together with a copy of the LaTeX +%% base system. You may however distribute the LaTeX base system without +%% such generated files. +%% +%% The list of all files belonging to the LaTeX base distribution is +%% given in the file `manifest.txt'. See also `legal.txt' for additional +%% information. +%% +%% \CharacterTable +%% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z +%% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z +%% Digits \0\1\2\3\4\5\6\7\8\9 +%% Exclamation \! Double quote \" Hash (number) \# +%% Dollar \$ Percent \% Ampersand \& +%% Acute accent \' Left paren \( Right paren \) +%% Asterisk \* Plus \+ Comma \, +%% Minus \- Point \. Solidus \/ +%% Colon \: Semicolon \; Less than \< +%% Equals \= Greater than \> Question mark \? +%% Commercial at \@ Left bracket \[ Backslash \\ +%% Right bracket \] Circumflex \^ Underscore \_ +%% Grave accent \` Left brace \{ Vertical bar \| +%% Right brace \} Tilde \~} +\NeedsTeXFormat{LaTeX2e}[1995/12/01] +\ProvidesClass{article} + [2000/05/19 v1.4b + Standard LaTeX document class] +\newcommand\@ptsize{} +\newif\if@restonecol +\newif\if@titlepage +\@titlepagefalse +\if@compatibility\else +\DeclareOption{a4paper} + {\setlength\paperheight {297mm}% + \setlength\paperwidth {210mm}} +\DeclareOption{a5paper} + {\setlength\paperheight {210mm}% + \setlength\paperwidth {148mm}} +\DeclareOption{b5paper} + {\setlength\paperheight {250mm}% + \setlength\paperwidth {176mm}} +\DeclareOption{letterpaper} + {\setlength\paperheight {11in}% + \setlength\paperwidth {8.5in}} +\DeclareOption{legalpaper} + {\setlength\paperheight {14in}% + \setlength\paperwidth {8.5in}} +\DeclareOption{executivepaper} + {\setlength\paperheight {10.5in}% + \setlength\paperwidth {7.25in}} +\DeclareOption{landscape} + {\setlength\@tempdima {\paperheight}% + \setlength\paperheight {\paperwidth}% + \setlength\paperwidth {\@tempdima}} +\fi +\if@compatibility + \renewcommand\@ptsize{0} +\else +\DeclareOption{10pt}{\renewcommand\@ptsize{0}} +\fi +\DeclareOption{11pt}{\renewcommand\@ptsize{1}} +\DeclareOption{12pt}{\renewcommand\@ptsize{2}} +\if@compatibility\else +\DeclareOption{oneside}{\@twosidefalse \@mparswitchfalse} +\fi +\DeclareOption{twoside}{\@twosidetrue \@mparswitchtrue} +\DeclareOption{draft}{\setlength\overfullrule{5pt}} +\if@compatibility\else +\DeclareOption{final}{\setlength\overfullrule{0pt}} +\fi +\DeclareOption{titlepage}{\@titlepagetrue} +\if@compatibility\else +\DeclareOption{notitlepage}{\@titlepagefalse} +\fi +\if@compatibility\else +\DeclareOption{onecolumn}{\@twocolumnfalse} +\fi +\DeclareOption{twocolumn}{\@twocolumntrue} +\DeclareOption{leqno}{\input{leqno.clo}} +\DeclareOption{fleqn}{\input{fleqn.clo}} +\DeclareOption{openbib}{% + \AtEndOfPackage{% + \renewcommand\@openbib@code{% + \advance\leftmargin\bibindent + \itemindent -\bibindent + \listparindent \itemindent + \parsep \z@ + }% + \renewcommand\newblock{\par}}% +} +\ExecuteOptions{letterpaper,10pt,oneside,onecolumn,final} +\ProcessOptions +\input{size1\@ptsize.clo} +\setlength\lineskip{1\p@} +\setlength\normallineskip{1\p@} +\renewcommand\baselinestretch{} +\setlength\parskip{0\p@ \@plus \p@} +\@lowpenalty 51 +\@medpenalty 151 +\@highpenalty 301 +\setcounter{topnumber}{2} +\renewcommand\topfraction{.7} +\setcounter{bottomnumber}{1} +\renewcommand\bottomfraction{.3} +\setcounter{totalnumber}{3} +\renewcommand\textfraction{.2} +\renewcommand\floatpagefraction{.5} +\setcounter{dbltopnumber}{2} +\renewcommand\dbltopfraction{.7} +\renewcommand\dblfloatpagefraction{.5} +\if@twoside + \def\ps@headings{% + \let\@oddfoot\@empty\let\@evenfoot\@empty + \def\@evenhead{\thepage\hfil\slshape\leftmark}% + \def\@oddhead{{\slshape\rightmark}\hfil\thepage}% + \let\@mkboth\markboth + \def\sectionmark##1{% + \markboth {\MakeUppercase{% + \ifnum \c@secnumdepth >\z@ + \thesection\quad + \fi + ##1}}{}}% + \def\subsectionmark##1{% + \markright {% + \ifnum \c@secnumdepth >\@ne + \thesubsection\quad + \fi + ##1}}} +\else + \def\ps@headings{% + \let\@oddfoot\@empty + \def\@oddhead{{\slshape\rightmark}\hfil\thepage}% + \let\@mkboth\markboth + \def\sectionmark##1{% + \markright {\MakeUppercase{% + \ifnum \c@secnumdepth >\m@ne + \thesection\quad + \fi + ##1}}}} +\fi +\def\ps@myheadings{% + \let\@oddfoot\@empty\let\@evenfoot\@empty + \def\@evenhead{\thepage\hfil\slshape\leftmark}% + \def\@oddhead{{\slshape\rightmark}\hfil\thepage}% + \let\@mkboth\@gobbletwo + \let\sectionmark\@gobble + \let\subsectionmark\@gobble + } + \if@titlepage + \newcommand\maketitle{\begin{titlepage}% + \let\footnotesize\small + \let\footnoterule\relax + \let \footnote \thanks + \null\vfil + \vskip 60\p@ + \begin{center}% + {\LARGE \@title \par}% + \vskip 3em% + {\large + \lineskip .75em% + \begin{tabular}[t]{c}% + \@author + \end{tabular}\par}% + \vskip 1.5em% + {\large \@date \par}% % Set date in \large size. + \end{center}\par + \@thanks + \vfil\null + \end{titlepage}% + \setcounter{footnote}{0}% + \global\let\thanks\relax + \global\let\maketitle\relax + \global\let\@thanks\@empty + \global\let\@author\@empty + \global\let\@date\@empty + \global\let\@title\@empty + \global\let\title\relax + \global\let\author\relax + \global\let\date\relax + \global\let\and\relax +} +\else +\newcommand\maketitle{\par + \begingroup + \renewcommand\thefootnote{\@fnsymbol\c@footnote}% + \def\@makefnmark{\rlap{\@textsuperscript{\normalfont\@thefnmark}}}% + \long\def\@makefntext##1{\parindent 1em\noindent + \hb@xt@1.8em{% + \hss\@textsuperscript{\normalfont\@thefnmark}}##1}% + \if@twocolumn + \ifnum \col@number=\@ne + \@maketitle + \else + \twocolumn[\@maketitle]% + \fi + \else + \newpage + \global\@topnum\z@ % Prevents figures from going at top of page. + \@maketitle + \fi + \thispagestyle{plain}\@thanks + \endgroup + \setcounter{footnote}{0}% + \global\let\thanks\relax + \global\let\maketitle\relax + \global\let\@maketitle\relax + \global\let\@thanks\@empty + \global\let\@author\@empty + \global\let\@date\@empty + \global\let\@title\@empty + \global\let\title\relax + \global\let\author\relax + \global\let\date\relax + \global\let\and\relax +} +\def\@maketitle{% + \newpage + \null + \vskip 2em% + \begin{center}% + \let \footnote \thanks + {\LARGE \@title \par}% + \vskip 1.5em% + {\large + \lineskip .5em% + \begin{tabular}[t]{c}% + \@author + \end{tabular}\par}% + \vskip 1em% + {\large \@date}% + \end{center}% + \par + \vskip 1.5em} +\fi +\setcounter{secnumdepth}{3} +\newcounter {part} +\newcounter {section} +\newcounter {subsection}[section] +\newcounter {subsubsection}[subsection] +\newcounter {paragraph}[subsubsection] +\newcounter {subparagraph}[paragraph] +\renewcommand \thepart {\@Roman\c@part} +\renewcommand \thesection {\@arabic\c@section} +\renewcommand\thesubsection {\thesection.\@arabic\c@subsection} +\renewcommand\thesubsubsection{\thesubsection .\@arabic\c@subsubsection} +\renewcommand\theparagraph {\thesubsubsection.\@arabic\c@paragraph} +\renewcommand\thesubparagraph {\theparagraph.\@arabic\c@subparagraph} +\newcommand\part{% + \if@noskipsec \leavevmode \fi + \par + \addvspace{4ex}% + \@afterindentfalse + \secdef\@part\@spart} + +\def\@part[#1]#2{% + \ifnum \c@secnumdepth >\m@ne + \refstepcounter{part}% + \addcontentsline{toc}{part}{\thepart\hspace{1em}#1}% + \else + \addcontentsline{toc}{part}{#1}% + \fi + {\parindent \z@ \raggedright + \interlinepenalty \@M + \normalfont + \ifnum \c@secnumdepth >\m@ne + \Large\bfseries \partname~\thepart + \par\nobreak + \fi + \huge \bfseries #2% + \markboth{}{}\par}% + \nobreak + \vskip 3ex + \@afterheading} +\def\@spart#1{% + {\parindent \z@ \raggedright + \interlinepenalty \@M + \normalfont + \huge \bfseries #1\par}% + \nobreak + \vskip 3ex + \@afterheading} +\newcommand\section{\@startsection {section}{1}{\z@}% + {-3.5ex \@plus -1ex \@minus -.2ex}% + {2.3ex \@plus.2ex}% + {\normalfont\Large\bfseries}} +\newcommand\subsection{\@startsection{subsection}{2}{\z@}% + {-3.25ex\@plus -1ex \@minus -.2ex}% + {1.5ex \@plus .2ex}% + {\normalfont\large\bfseries}} +\newcommand\subsubsection{\@startsection{subsubsection}{3}{\z@}% + {-3.25ex\@plus -1ex \@minus -.2ex}% + {1.5ex \@plus .2ex}% + {\normalfont\normalsize\bfseries}} +\newcommand\paragraph{\@startsection{paragraph}{4}{\z@}% + {3.25ex \@plus1ex \@minus.2ex}% + {-1em}% + {\normalfont\normalsize\bfseries}} +\newcommand\subparagraph{\@startsection{subparagraph}{5}{\parindent}% + {3.25ex \@plus1ex \@minus .2ex}% + {-1em}% + {\normalfont\normalsize\bfseries}} +\if@twocolumn + \setlength\leftmargini {2em} +\else + \setlength\leftmargini {2.5em} +\fi +\leftmargin \leftmargini +\setlength\leftmarginii {2.2em} +\setlength\leftmarginiii {1.87em} +\setlength\leftmarginiv {1.7em} +\if@twocolumn + \setlength\leftmarginv {.5em} + \setlength\leftmarginvi {.5em} +\else + \setlength\leftmarginv {1em} + \setlength\leftmarginvi {1em} +\fi +\setlength \labelsep {.5em} +\setlength \labelwidth{\leftmargini} +\addtolength\labelwidth{-\labelsep} +\@beginparpenalty -\@lowpenalty +\@endparpenalty -\@lowpenalty +\@itempenalty -\@lowpenalty +\renewcommand\theenumi{\@arabic\c@enumi} +\renewcommand\theenumii{\@alph\c@enumii} +\renewcommand\theenumiii{\@roman\c@enumiii} +\renewcommand\theenumiv{\@Alph\c@enumiv} +\newcommand\labelenumi{\theenumi.} +\newcommand\labelenumii{(\theenumii)} +\newcommand\labelenumiii{\theenumiii.} +\newcommand\labelenumiv{\theenumiv.} +\renewcommand\p@enumii{\theenumi} +\renewcommand\p@enumiii{\theenumi(\theenumii)} +\renewcommand\p@enumiv{\p@enumiii\theenumiii} +\newcommand\labelitemi{\textbullet} +\newcommand\labelitemii{\normalfont\bfseries \textendash} +\newcommand\labelitemiii{\textasteriskcentered} +\newcommand\labelitemiv{\textperiodcentered} +\newenvironment{description} + {\list{}{\labelwidth\z@ \itemindent-\leftmargin + \let\makelabel\descriptionlabel}} + {\endlist} +\newcommand*\descriptionlabel[1]{\hspace\labelsep + \normalfont\bfseries #1} +\if@titlepage + \newenvironment{abstract}{% + \titlepage + \null\vfil + \@beginparpenalty\@lowpenalty + \begin{center}% + \bfseries \abstractname + \@endparpenalty\@M + \end{center}}% + {\par\vfil\null\endtitlepage} +\else + \newenvironment{abstract}{% + \if@twocolumn + \section*{\abstractname}% + \else + \small + \begin{center}% + {\bfseries \abstractname\vspace{-.5em}\vspace{\z@}}% + \end{center}% + \quotation + \fi} + {\if@twocolumn\else\endquotation\fi} +\fi +\newenvironment{verse} + {\let\\\@centercr + \list{}{\itemsep \z@ + \itemindent -1.5em% + \listparindent\itemindent + \rightmargin \leftmargin + \advance\leftmargin 1.5em}% + \item\relax} + {\endlist} +\newenvironment{quotation} + {\list{}{\listparindent 1.5em% + \itemindent \listparindent + \rightmargin \leftmargin + \parsep \z@ \@plus\p@}% + \item\relax} + {\endlist} +\newenvironment{quote} + {\list{}{\rightmargin\leftmargin}% + \item\relax} + {\endlist} +\if@compatibility +\newenvironment{titlepage} + {% + \if@twocolumn + \@restonecoltrue\onecolumn + \else + \@restonecolfalse\newpage + \fi + \thispagestyle{empty}% + \setcounter{page}\z@ + }% + {\if@restonecol\twocolumn \else \newpage \fi + } +\else +\newenvironment{titlepage} + {% + \if@twocolumn + \@restonecoltrue\onecolumn + \else + \@restonecolfalse\newpage + \fi + \thispagestyle{empty}% + \setcounter{page}\@ne + }% + {\if@restonecol\twocolumn \else \newpage \fi + \if@twoside\else + \setcounter{page}\@ne + \fi + } +\fi +\newcommand\appendix{\par + \setcounter{section}{0}% + \setcounter{subsection}{0}% + \gdef\thesection{\@Alph\c@section}} +\setlength\arraycolsep{5\p@} +\setlength\tabcolsep{6\p@} +\setlength\arrayrulewidth{.4\p@} +\setlength\doublerulesep{2\p@} +\setlength\tabbingsep{\labelsep} +\skip\@mpfootins = \skip\footins +\setlength\fboxsep{3\p@} +\setlength\fboxrule{.4\p@} +\renewcommand \theequation {\@arabic\c@equation} +\newcounter{figure} +\renewcommand \thefigure {\@arabic\c@figure} +\def\fps@figure{tbp} +\def\ftype@figure{1} +\def\ext@figure{lof} +\def\fnum@figure{\figurename~\thefigure} +\newenvironment{figure} + {\@float{figure}} + {\end@float} +\newenvironment{figure*} + {\@dblfloat{figure}} + {\end@dblfloat} +\newcounter{table} +\renewcommand\thetable{\@arabic\c@table} +\def\fps@table{tbp} +\def\ftype@table{2} +\def\ext@table{lot} +\def\fnum@table{\tablename~\thetable} +\newenvironment{table} + {\@float{table}} + {\end@float} +\newenvironment{table*} + {\@dblfloat{table}} + {\end@dblfloat} +\newlength\abovecaptionskip +\newlength\belowcaptionskip +\setlength\abovecaptionskip{10\p@} +\setlength\belowcaptionskip{0\p@} +\long\def\@makecaption#1#2{% + \vskip\abovecaptionskip + \sbox\@tempboxa{#1: #2}% + \ifdim \wd\@tempboxa >\hsize + #1: #2\par + \else + \global \@minipagefalse + \hb@xt@\hsize{\hfil\box\@tempboxa\hfil}% + \fi + \vskip\belowcaptionskip} +\DeclareOldFontCommand{\rm}{\normalfont\rmfamily}{\mathrm} +\DeclareOldFontCommand{\sf}{\normalfont\sffamily}{\mathsf} +\DeclareOldFontCommand{\tt}{\normalfont\ttfamily}{\mathtt} +\DeclareOldFontCommand{\bf}{\normalfont\bfseries}{\mathbf} +\DeclareOldFontCommand{\it}{\normalfont\itshape}{\mathit} +\DeclareOldFontCommand{\sl}{\normalfont\slshape}{\@nomath\sl} +\DeclareOldFontCommand{\sc}{\normalfont\scshape}{\@nomath\sc} +\DeclareRobustCommand*\cal{\@fontswitch\relax\mathcal} +\DeclareRobustCommand*\mit{\@fontswitch\relax\mathnormal} +\newcommand\@pnumwidth{1.55em} +\newcommand\@tocrmarg{2.55em} +\newcommand\@dotsep{4.5} +\setcounter{tocdepth}{3} +\newcommand\tableofcontents{% + \section*{\contentsname + \@mkboth{% + \MakeUppercase\contentsname}{\MakeUppercase\contentsname}}% + \@starttoc{toc}% + } +\newcommand*\l@part[2]{% + \ifnum \c@tocdepth >-2\relax + \addpenalty\@secpenalty + \addvspace{2.25em \@plus\p@}% + \begingroup + \parindent \z@ \rightskip \@pnumwidth + \parfillskip -\@pnumwidth + {\leavevmode + \large \bfseries #1\hfil \hb@xt@\@pnumwidth{\hss #2}}\par + \nobreak + \if@compatibility + \global\@nobreaktrue + \everypar{\global\@nobreakfalse\everypar{}}% + \fi + \endgroup + \fi} +\newcommand*\l@section[2]{% + \ifnum \c@tocdepth >\z@ + \addpenalty\@secpenalty + \addvspace{1.0em \@plus\p@}% + \setlength\@tempdima{1.5em}% + \begingroup + \parindent \z@ \rightskip \@pnumwidth + \parfillskip -\@pnumwidth + \leavevmode \bfseries + \advance\leftskip\@tempdima + \hskip -\leftskip + #1\nobreak\hfil \nobreak\hb@xt@\@pnumwidth{\hss #2}\par + \endgroup + \fi} +\newcommand*\l@subsection{\@dottedtocline{2}{1.5em}{2.3em}} +\newcommand*\l@subsubsection{\@dottedtocline{3}{3.8em}{3.2em}} +\newcommand*\l@paragraph{\@dottedtocline{4}{7.0em}{4.1em}} 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+\newcommand\listfigurename{List of Figures} +\newcommand\listtablename{List of Tables} +\newcommand\refname{References} +\newcommand\indexname{Index} +\newcommand\figurename{\small Figure} +\newcommand\tablename{Table} +\newcommand\partname{Part} +\newcommand\appendixname{Appendix} +\newcommand\abstractname{Abstract} +\def\today{\ifcase\month\or + January\or February\or March\or April\or May\or June\or + July\or August\or September\or October\or November\or December\fi + \space\number\day, \number\year} +\setlength\columnsep{10\p@} +\setlength\columnseprule{0\p@} +\pagestyle{plain} +\pagenumbering{arabic} +\if@twoside +\else + \raggedbottom +\fi +\if@twocolumn + \twocolumn + \sloppy + \flushbottom +\else + \onecolumn +\fi +\endinput +%% +%% End of file `article.cls'. diff --git a/crCOUCHOT14/conclusion.tex b/crCOUCHOT14/conclusion.tex new file mode 100644 index 0000000..f0522c7 --- /dev/null +++ b/crCOUCHOT14/conclusion.tex @@ -0,0 +1,17 @@ +Before this work, the second class of +chaos-based PRNG $\textit{CIPRNG}_f^2$ was robust against +batteries of statistical tests and was abusively said to be chaotic. +This work has formally established the proof that +the $\textit{CIPRNG}_f^2$ is chaotic according to the Devaney +definition for some well-chosen functions $f$. +The chaos condition is expressed as a necessary and sufficient condition +on a graph of iterations: this one has to be strongly connected. + +It has thus bridged the gap between the need of true chaos for some +applications and the practical efficiency. +In a future work, we plan to study sufficient conditions on $f$ to +observe this +connectivity +and to study computed functions in the perspective +of mixing time to improve their practical efficiency. + diff --git a/crCOUCHOT14/example.bib b/crCOUCHOT14/example.bib new file mode 100644 index 0000000..49a8286 --- /dev/null +++ b/crCOUCHOT14/example.bib @@ -0,0 +1,19 @@ + +@INPROCEEDINGS{Moore99, + AUTHOR = "R. Moore and J. Lopes", + TITLE = "Paper templates", + BOOKTITLE = "TEMPLATE'06, 1st International Conference on Template Production", + YEAR = "1999", + publisher = "SCITEPRESS", + file = F +} + +@BOOK{Smith98, + AUTHOR = "J. Smith", + TITLE = "The Book", + PUBLISHER = "The publishing company", + YEAR = "1998", + address = "London", + edition = "2nd", + file = F +} diff --git a/crCOUCHOT14/graphe1.pdf b/crCOUCHOT14/graphe1.pdf new file mode 100644 index 0000000..0e0e765 Binary files /dev/null and b/crCOUCHOT14/graphe1.pdf differ diff --git a/crCOUCHOT14/graphe2.pdf b/crCOUCHOT14/graphe2.pdf new file mode 100644 index 0000000..9ea5f8e Binary files /dev/null and b/crCOUCHOT14/graphe2.pdf differ diff --git a/crCOUCHOT14/intro.tex b/crCOUCHOT14/intro.tex new file mode 100644 index 0000000..7b342b6 --- /dev/null +++ b/crCOUCHOT14/intro.tex @@ -0,0 +1,71 @@ + +From the last two decades, many researchers have investigated the use +of chaotic systems to build pseudorandom +sequences~\cite{915396,915385,5376454}. Two main features can +intuitively explain this interest: first of all, chaotic systems have +unpredictable or disorder-like behavior which is needed for producing +complex sequences. Furthermore, such systems are extremely sensitive +to the initial states too: a tiny difference in the input +may lead to dramatic changes in output. + +Moreover, the property of chaos is often reduced to iterate a +\emph{chaotic} function, namely the logistic map\footnote{The logistic +map is defined by $X^0 \in [0,1], X^{n+1} = \mu X^n(1-X^n), \mu \in +[0,4]$.}~\cite{915396,915385}, the Arnolds cat map\footnote{Discrete +Arnolds cat map is defined by $(X^0, Y^0)\in [0,N]^2, X^{n+1} = 2 Y^n ++ X^n$ mod $N$, $Y^{n+1} = X^n+Y^n$ mod $N$.}~\cite{5376454}\ldots +Au\-thors +are thus focused on finding parameters of such kind of functions which +are the most suitable for generating random-like sequences. More +precisely, they have thus to find function parameters that avoid +parasitic attractors and that lead to a uniform distribution of the +output. To check how accurate are their generated +sequences~\cite{bfgw13:ij}, authors are then left to submit their +chaos-based PRNG with good parameters on statistical batteries of +tests~\cite{DBLP:journals/corr/abs-1112-5239}, namely: +DieHARD~\cite{Marsaglia1996}, NIST~\cite{Nist10}, and +TestU01~\cite{LEcuyerS07}. + + + +Devaney has formalized~\cite{Devaney} the fundamental properties of +the chaotic maps, namely: sensitive dependence on initial conditions, +transitivity, and density of periodic points. For short, a system is +sensitive to initial conditions if any point contains, in any +neighborhood, another point with a completely different future +trajectory. Topological transitivity is established when, for any +element, any neighborhood of its future evolution eventually overlaps +with any other open set. On the contrary, a dense set of periodic +points is an element of regularity that a chaotic dynamical system has +to exhibit. However, because of the finiteness of the memory of a +computer, only a kind of discrete chaos is generated. This induces +that chaotic properties, which could have been proven on $\Reels$, can +however be lost on floating point numbers, which is the interpretation +domain of $\Reels$. + +To avoid this loss of chaos, we had constructed chaos-based PRNGs +that iterate a continuous functions $G_f$ defined on the discrete +domain $\llbracket 1 ; n \rrbracket^{\Nats} \times \{0,1\}^n$ where +$f$ is a Boolean function (\textit{i.e.}, $f : \{0,1\}^n \rightarrow +\{0,1\}^n$). These PRNGs are named +$\textit{CIPRNG}_f^1(u)$~\cite{bgw09:ip,guyeuxTaiwan10}, +$\textit{CIPRNG}_f^2(u,v)$~\cite{wbg10:ip}, and +$\textit{XOR~CIPRNG}(S)$~\cite{DBLP:journals/corr/abs-1112-5239}, +where \textit{CI} stands for \emph{Chaotic Iterations}, which have +been particularized according to the function they iterate. + +Chaotic properties have been well established for both the +$\textit{XOR~CIPRNG}$ and $\textit{CIPRNG}_f^1(u)$ under certain +conditions for the iteration function $f$, it has been formerly +deduced that it was the case too for the whole $\textit{CIPRNG}_f^2$ +category of generators. However, contrarily to what has been too much +rapidly deduced, this claim is not obvious (a subsequence of a chaotic +sequence is not necessarily a chaotic sequence too) and it +necessitates a rigorous proof, which is the aim of this article. + +The remainder of the paper is organized as follows. +Section~\ref{sec:notations} recalls definitions of chaos properties +and of the family of \textit{CIPRNG}. Section~\ref{sec:wellchosen} +gives the complete proof of chaos for the $\textit{CIPRNG}_f^2$ +category. This is the main contribution of this work. The paper ends +with a conclusion section where intended future work is presented. diff --git a/crCOUCHOT14/iter_f0-eps-converted-to.pdf b/crCOUCHOT14/iter_f0-eps-converted-to.pdf new file mode 100644 index 0000000..2d366f7 Binary files /dev/null and b/crCOUCHOT14/iter_f0-eps-converted-to.pdf differ diff --git a/crCOUCHOT14/iter_f0.dot b/crCOUCHOT14/iter_f0.dot new file mode 100644 index 0000000..5343192 --- /dev/null +++ b/crCOUCHOT14/iter_f0.dot @@ -0,0 +1,27 @@ +digraph { + graph [rankdir=LR] + 000 -> 000; + 000 -> 010; + 000 -> 001; + 010 -> 010; + 010 -> 110; + 010 -> 011; + 001 -> 000; + 001 -> 001; + 001 -> 101; + 101 -> 101; + 101 -> 100; + 101 -> 111; + 110 -> 110; + 110 -> 100; + 110 -> 111; + 011 -> 010; + 011 -> 001; + 011 -> 011; + 100 -> 000; + 100 -> 101; + 100 -> 100; + 111 -> 110; + 111 -> 011; + 111 -> 111; +} diff --git a/crCOUCHOT14/iter_f0.eps b/crCOUCHOT14/iter_f0.eps new file mode 100644 index 0000000..6962b81 --- /dev/null +++ b/crCOUCHOT14/iter_f0.eps @@ -0,0 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Double quote \" Hash (number) \# +%% Dollar \$ Percent \% Ampersand \& +%% Acute accent \' Left paren \( Right paren \) +%% Asterisk \* Plus \+ Comma \, +%% Minus \- Point \. Solidus \/ +%% Colon \: Semicolon \; Less than \< +%% Equals \= Greater than \> Question mark \? +%% Commercial at \@ Left bracket \[ Backslash \\ +%% Right bracket \] Circumflex \^ Underscore \_ +%% Grave accent \` Left brace \{ Vertical bar \| +%% Right brace \} Tilde \~} +%% +\NeedsTeXFormat{LaTeX2e}[1995/12/01] +\ProvidesClass{llncs}[2010/07/12 v2.17 +^^J LaTeX document class for Lecture Notes in Computer Science] +% Options +\let\if@envcntreset\iffalse +\DeclareOption{envcountreset}{\let\if@envcntreset\iftrue} +\DeclareOption{citeauthoryear}{\let\citeauthoryear=Y} +\DeclareOption{oribibl}{\let\oribibl=Y} +\let\if@custvec\iftrue +\DeclareOption{orivec}{\let\if@custvec\iffalse} +\let\if@envcntsame\iffalse +\DeclareOption{envcountsame}{\let\if@envcntsame\iftrue} +\let\if@envcntsect\iffalse +\DeclareOption{envcountsect}{\let\if@envcntsect\iftrue} +\let\if@runhead\iffalse +\DeclareOption{runningheads}{\let\if@runhead\iftrue} + +\let\if@openright\iftrue +\let\if@openbib\iffalse +\DeclareOption{openbib}{\let\if@openbib\iftrue} + +% languages +\let\switcht@@therlang\relax +\def\ds@deutsch{\def\switcht@@therlang{\switcht@deutsch}} +\def\ds@francais{\def\switcht@@therlang{\switcht@francais}} + +\DeclareOption*{\PassOptionsToClass{\CurrentOption}{article}} + +\ProcessOptions + +\LoadClass[twoside]{article} +\RequirePackage{multicol} % needed for the list of participants, index +\RequirePackage{aliascnt} + +\setlength{\textwidth}{12.2cm} +\setlength{\textheight}{19.3cm} +\renewcommand\@pnumwidth{2em} +\renewcommand\@tocrmarg{3.5em} +% +\def\@dottedtocline#1#2#3#4#5{% + \ifnum #1>\c@tocdepth \else + \vskip \z@ \@plus.2\p@ + {\leftskip #2\relax \rightskip \@tocrmarg \advance\rightskip by 0pt plus 2cm + \parfillskip -\rightskip \pretolerance=10000 + \parindent #2\relax\@afterindenttrue + \interlinepenalty\@M + \leavevmode + \@tempdima #3\relax + \advance\leftskip \@tempdima \null\nobreak\hskip -\leftskip + {#4}\nobreak + \leaders\hbox{$\m@th + \mkern \@dotsep mu\hbox{.}\mkern \@dotsep + mu$}\hfill + \nobreak + \hb@xt@\@pnumwidth{\hfil\normalfont \normalcolor #5}% + \par}% + \fi} +% +\def\switcht@albion{% +\def\abstractname{Abstract.} +\def\ackname{Acknowledgement.} +\def\andname{and} +\def\lastandname{\unskip, and} +\def\appendixname{Appendix} +\def\chaptername{Chapter} +\def\claimname{Claim} +\def\conjecturename{Conjecture} +\def\contentsname{Table of Contents} +\def\corollaryname{Corollary} +\def\definitionname{Definition} +\def\examplename{Example} +\def\exercisename{Exercise} +\def\figurename{Fig.} +\def\keywordname{{\bf Keywords:}} +\def\indexname{Index} +\def\lemmaname{Lemma} +\def\contriblistname{List of Contributors} +\def\listfigurename{List of Figures} +\def\listtablename{List of Tables} +\def\mailname{{\it Correspondence to\/}:} +\def\noteaddname{Note added in proof} +\def\notename{Note} +\def\partname{Part} +\def\problemname{Problem} +\def\proofname{Proof} +\def\propertyname{Property} +\def\propositionname{Proposition} +\def\questionname{Question} +\def\remarkname{Remark} +\def\seename{see} +\def\solutionname{Solution} +\def\subclassname{{\it Subject Classifications\/}:} +\def\tablename{Table} +\def\theoremname{Theorem}} +\switcht@albion +% Names of theorem like environments are already defined +% but must be translated if another language is chosen +% +% French section +\def\switcht@francais{%\typeout{On parle francais.}% + \def\abstractname{R\'esum\'e.}% + \def\ackname{Remerciements.}% + \def\andname{et}% + \def\lastandname{ et}% + \def\appendixname{Appendice} + \def\chaptername{Chapitre}% + \def\claimname{Pr\'etention}% + \def\conjecturename{Hypoth\`ese}% + \def\contentsname{Table des mati\`eres}% + \def\corollaryname{Corollaire}% + \def\definitionname{D\'efinition}% + \def\examplename{Exemple}% + \def\exercisename{Exercice}% + \def\figurename{Fig.}% + \def\keywordname{{\bf Mots-cl\'e:}} + \def\indexname{Index} + \def\lemmaname{Lemme}% + \def\contriblistname{Liste des contributeurs} + \def\listfigurename{Liste des figures}% + \def\listtablename{Liste des tables}% + \def\mailname{{\it Correspondence to\/}:} + \def\noteaddname{Note ajout\'ee \`a l'\'epreuve}% + \def\notename{Remarque}% + \def\partname{Partie}% + \def\problemname{Probl\`eme}% + \def\proofname{Preuve}% + \def\propertyname{Caract\'eristique}% +%\def\propositionname{Proposition}% + \def\questionname{Question}% + \def\remarkname{Remarque}% + \def\seename{voir} + \def\solutionname{Solution}% + \def\subclassname{{\it Subject Classifications\/}:} + \def\tablename{Tableau}% + \def\theoremname{Th\'eor\`eme}% +} +% +% German section +\def\switcht@deutsch{%\typeout{Man spricht deutsch.}% + \def\abstractname{Zusammenfassung.}% + \def\ackname{Danksagung.}% + \def\andname{und}% + \def\lastandname{ und}% + \def\appendixname{Anhang}% + \def\chaptername{Kapitel}% + \def\claimname{Behauptung}% + \def\conjecturename{Hypothese}% + \def\contentsname{Inhaltsverzeichnis}% + \def\corollaryname{Korollar}% +%\def\definitionname{Definition}% + \def\examplename{Beispiel}% + \def\exercisename{\"Ubung}% + \def\figurename{Abb.}% + \def\keywordname{{\bf Schl\"usselw\"orter:}} + \def\indexname{Index} +%\def\lemmaname{Lemma}% + \def\contriblistname{Mitarbeiter} + \def\listfigurename{Abbildungsverzeichnis}% + \def\listtablename{Tabellenverzeichnis}% + \def\mailname{{\it Correspondence to\/}:} + \def\noteaddname{Nachtrag}% + \def\notename{Anmerkung}% + \def\partname{Teil}% +%\def\problemname{Problem}% + \def\proofname{Beweis}% + \def\propertyname{Eigenschaft}% +%\def\propositionname{Proposition}% + \def\questionname{Frage}% + \def\remarkname{Anmerkung}% + \def\seename{siehe} + \def\solutionname{L\"osung}% + \def\subclassname{{\it Subject Classifications\/}:} + \def\tablename{Tabelle}% +%\def\theoremname{Theorem}% +} + +% Ragged bottom for the actual page +\def\thisbottomragged{\def\@textbottom{\vskip\z@ plus.0001fil +\global\let\@textbottom\relax}} + +\renewcommand\small{% + \@setfontsize\small\@ixpt{11}% + \abovedisplayskip 8.5\p@ \@plus3\p@ \@minus4\p@ + \abovedisplayshortskip \z@ \@plus2\p@ + \belowdisplayshortskip 4\p@ \@plus2\p@ \@minus2\p@ + \def\@listi{\leftmargin\leftmargini + \parsep 0\p@ \@plus1\p@ \@minus\p@ + \topsep 8\p@ \@plus2\p@ \@minus4\p@ + \itemsep0\p@}% + \belowdisplayskip \abovedisplayskip +} + +\frenchspacing +\widowpenalty=10000 +\clubpenalty=10000 + +\setlength\oddsidemargin {63\p@} +\setlength\evensidemargin {63\p@} +\setlength\marginparwidth {90\p@} + +\setlength\headsep {16\p@} + +\setlength\footnotesep{7.7\p@} +\setlength\textfloatsep{8mm\@plus 2\p@ \@minus 4\p@} +\setlength\intextsep {8mm\@plus 2\p@ \@minus 2\p@} + +\setcounter{secnumdepth}{2} + +\newcounter {chapter} +\renewcommand\thechapter {\@arabic\c@chapter} + +\newif\if@mainmatter \@mainmattertrue +\newcommand\frontmatter{\cleardoublepage + \@mainmatterfalse\pagenumbering{Roman}} +\newcommand\mainmatter{\cleardoublepage + \@mainmattertrue\pagenumbering{arabic}} +\newcommand\backmatter{\if@openright\cleardoublepage\else\clearpage\fi + \@mainmatterfalse} + +\renewcommand\part{\cleardoublepage + \thispagestyle{empty}% + \if@twocolumn + \onecolumn + \@tempswatrue + \else + \@tempswafalse + \fi + \null\vfil + \secdef\@part\@spart} + +\def\@part[#1]#2{% + \ifnum \c@secnumdepth >-2\relax + \refstepcounter{part}% + \addcontentsline{toc}{part}{\thepart\hspace{1em}#1}% + \else + \addcontentsline{toc}{part}{#1}% + \fi + \markboth{}{}% + {\centering + \interlinepenalty \@M + \normalfont + \ifnum \c@secnumdepth >-2\relax + \huge\bfseries \partname~\thepart + \par + \vskip 20\p@ + \fi + \Huge \bfseries #2\par}% + \@endpart} +\def\@spart#1{% + {\centering + \interlinepenalty \@M + \normalfont + \Huge \bfseries #1\par}% + \@endpart} +\def\@endpart{\vfil\newpage + \if@twoside + \null + \thispagestyle{empty}% + \newpage + \fi + \if@tempswa + \twocolumn + \fi} + +\newcommand\chapter{\clearpage + \thispagestyle{empty}% + \global\@topnum\z@ + \@afterindentfalse + \secdef\@chapter\@schapter} +\def\@chapter[#1]#2{\ifnum \c@secnumdepth >\m@ne + \if@mainmatter + \refstepcounter{chapter}% + \typeout{\@chapapp\space\thechapter.}% + \addcontentsline{toc}{chapter}% + {\protect\numberline{\thechapter}#1}% + \else + \addcontentsline{toc}{chapter}{#1}% + \fi + \else + \addcontentsline{toc}{chapter}{#1}% + \fi + \chaptermark{#1}% + \addtocontents{lof}{\protect\addvspace{10\p@}}% + \addtocontents{lot}{\protect\addvspace{10\p@}}% + \if@twocolumn + \@topnewpage[\@makechapterhead{#2}]% + \else + \@makechapterhead{#2}% + \@afterheading + \fi} +\def\@makechapterhead#1{% +% \vspace*{50\p@}% + {\centering + \ifnum \c@secnumdepth >\m@ne + \if@mainmatter + \large\bfseries \@chapapp{} \thechapter + \par\nobreak + \vskip 20\p@ + \fi + \fi + \interlinepenalty\@M + \Large \bfseries #1\par\nobreak + \vskip 40\p@ + }} +\def\@schapter#1{\if@twocolumn + \@topnewpage[\@makeschapterhead{#1}]% + \else + \@makeschapterhead{#1}% + \@afterheading + \fi} +\def\@makeschapterhead#1{% +% \vspace*{50\p@}% + {\centering + \normalfont + \interlinepenalty\@M + \Large \bfseries #1\par\nobreak + \vskip 40\p@ + }} + +\renewcommand\section{\@startsection{section}{1}{\z@}% + {-18\p@ \@plus -4\p@ \@minus -4\p@}% + {12\p@ \@plus 4\p@ \@minus 4\p@}% + {\normalfont\large\bfseries\boldmath + \rightskip=\z@ \@plus 8em\pretolerance=10000 }} +\renewcommand\subsection{\@startsection{subsection}{2}{\z@}% + {-18\p@ \@plus -4\p@ \@minus -4\p@}% + {8\p@ \@plus 4\p@ \@minus 4\p@}% + {\normalfont\normalsize\bfseries\boldmath + \rightskip=\z@ \@plus 8em\pretolerance=10000 }} +\renewcommand\subsubsection{\@startsection{subsubsection}{3}{\z@}% + {-18\p@ \@plus -4\p@ \@minus -4\p@}% + {-0.5em \@plus -0.22em \@minus -0.1em}% + {\normalfont\normalsize\bfseries\boldmath}} +\renewcommand\paragraph{\@startsection{paragraph}{4}{\z@}% + {-12\p@ \@plus -4\p@ \@minus -4\p@}% + {-0.5em \@plus -0.22em \@minus -0.1em}% + {\normalfont\normalsize\itshape}} +\renewcommand\subparagraph[1]{\typeout{LLNCS warning: You should not use + \string\subparagraph\space with this class}\vskip0.5cm +You should not use \verb|\subparagraph| with this class.\vskip0.5cm} + +\DeclareMathSymbol{\Gamma}{\mathalpha}{letters}{"00} +\DeclareMathSymbol{\Delta}{\mathalpha}{letters}{"01} +\DeclareMathSymbol{\Theta}{\mathalpha}{letters}{"02} +\DeclareMathSymbol{\Lambda}{\mathalpha}{letters}{"03} +\DeclareMathSymbol{\Xi}{\mathalpha}{letters}{"04} +\DeclareMathSymbol{\Pi}{\mathalpha}{letters}{"05} +\DeclareMathSymbol{\Sigma}{\mathalpha}{letters}{"06} +\DeclareMathSymbol{\Upsilon}{\mathalpha}{letters}{"07} +\DeclareMathSymbol{\Phi}{\mathalpha}{letters}{"08} +\DeclareMathSymbol{\Psi}{\mathalpha}{letters}{"09} +\DeclareMathSymbol{\Omega}{\mathalpha}{letters}{"0A} + +\let\footnotesize\small + +\if@custvec +\def\vec#1{\mathchoice{\mbox{\boldmath$\displaystyle#1$}} +{\mbox{\boldmath$\textstyle#1$}} +{\mbox{\boldmath$\scriptstyle#1$}} +{\mbox{\boldmath$\scriptscriptstyle#1$}}} +\fi + +\def\squareforqed{\hbox{\rlap{$\sqcap$}$\sqcup$}} +\def\qed{\ifmmode\squareforqed\else{\unskip\nobreak\hfil +\penalty50\hskip1em\null\nobreak\hfil\squareforqed +\parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi} + +\def\getsto{\mathrel{\mathchoice {\vcenter{\offinterlineskip +\halign{\hfil +$\displaystyle##$\hfil\cr\gets\cr\to\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr\gets +\cr\to\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr\gets +\cr\to\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr +\gets\cr\to\cr}}}}} +\def\lid{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil +$\displaystyle##$\hfil\cr<\cr\noalign{\vskip1.2pt}=\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr<\cr +\noalign{\vskip1.2pt}=\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr<\cr +\noalign{\vskip1pt}=\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr +<\cr +\noalign{\vskip0.9pt}=\cr}}}}} +\def\gid{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil +$\displaystyle##$\hfil\cr>\cr\noalign{\vskip1.2pt}=\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr>\cr +\noalign{\vskip1.2pt}=\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr>\cr +\noalign{\vskip1pt}=\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr +>\cr +\noalign{\vskip0.9pt}=\cr}}}}} +\def\grole{\mathrel{\mathchoice {\vcenter{\offinterlineskip +\halign{\hfil +$\displaystyle##$\hfil\cr>\cr\noalign{\vskip-1pt}<\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr +>\cr\noalign{\vskip-1pt}<\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr +>\cr\noalign{\vskip-0.8pt}<\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr +>\cr\noalign{\vskip-0.3pt}<\cr}}}}} +\def\bbbr{{\rm I\!R}} %reelle Zahlen +\def\bbbm{{\rm I\!M}} +\def\bbbn{{\rm I\!N}} %natuerliche Zahlen +\def\bbbf{{\rm I\!F}} +\def\bbbh{{\rm I\!H}} +\def\bbbk{{\rm I\!K}} +\def\bbbp{{\rm I\!P}} +\def\bbbone{{\mathchoice {\rm 1\mskip-4mu l} {\rm 1\mskip-4mu l} +{\rm 1\mskip-4.5mu l} {\rm 1\mskip-5mu l}}} +\def\bbbc{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm C$}\hbox{\hbox +to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}} +{\setbox0=\hbox{$\textstyle\rm C$}\hbox{\hbox +to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptstyle\rm C$}\hbox{\hbox +to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptscriptstyle\rm C$}\hbox{\hbox +to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}}}} +\def\bbbq{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm +Q$}\hbox{\raise +0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.8\ht0\hss}\box0}} +{\setbox0=\hbox{$\textstyle\rm Q$}\hbox{\raise +0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.8\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptstyle\rm Q$}\hbox{\raise +0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.7\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptscriptstyle\rm Q$}\hbox{\raise +0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.7\ht0\hss}\box0}}}} +\def\bbbt{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm +T$}\hbox{\hbox to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}} +{\setbox0=\hbox{$\textstyle\rm T$}\hbox{\hbox +to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptstyle\rm T$}\hbox{\hbox +to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptscriptstyle\rm T$}\hbox{\hbox +to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}}}} +\def\bbbs{{\mathchoice +{\setbox0=\hbox{$\displaystyle \rm S$}\hbox{\raise0.5\ht0\hbox +to0pt{\kern0.35\wd0\vrule height0.45\ht0\hss}\hbox +to0pt{\kern0.55\wd0\vrule height0.5\ht0\hss}\box0}} +{\setbox0=\hbox{$\textstyle \rm S$}\hbox{\raise0.5\ht0\hbox +to0pt{\kern0.35\wd0\vrule height0.45\ht0\hss}\hbox +to0pt{\kern0.55\wd0\vrule height0.5\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptstyle \rm S$}\hbox{\raise0.5\ht0\hbox +to0pt{\kern0.35\wd0\vrule height0.45\ht0\hss}\raise0.05\ht0\hbox +to0pt{\kern0.5\wd0\vrule height0.45\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptscriptstyle\rm S$}\hbox{\raise0.5\ht0\hbox +to0pt{\kern0.4\wd0\vrule height0.45\ht0\hss}\raise0.05\ht0\hbox +to0pt{\kern0.55\wd0\vrule height0.45\ht0\hss}\box0}}}} +\def\bbbz{{\mathchoice {\hbox{$\mathsf\textstyle Z\kern-0.4em Z$}} +{\hbox{$\mathsf\textstyle Z\kern-0.4em Z$}} +{\hbox{$\mathsf\scriptstyle Z\kern-0.3em Z$}} +{\hbox{$\mathsf\scriptscriptstyle Z\kern-0.2em Z$}}}} + +\let\ts\, + +\setlength\leftmargini {17\p@} +\setlength\leftmargin {\leftmargini} +\setlength\leftmarginii {\leftmargini} +\setlength\leftmarginiii {\leftmargini} +\setlength\leftmarginiv {\leftmargini} +\setlength \labelsep {.5em} +\setlength \labelwidth{\leftmargini} +\addtolength\labelwidth{-\labelsep} + +\def\@listI{\leftmargin\leftmargini + \parsep 0\p@ \@plus1\p@ \@minus\p@ + \topsep 8\p@ \@plus2\p@ \@minus4\p@ + \itemsep0\p@} +\let\@listi\@listI +\@listi +\def\@listii {\leftmargin\leftmarginii + \labelwidth\leftmarginii + \advance\labelwidth-\labelsep + \topsep 0\p@ \@plus2\p@ \@minus\p@} +\def\@listiii{\leftmargin\leftmarginiii + \labelwidth\leftmarginiii + \advance\labelwidth-\labelsep + \topsep 0\p@ \@plus\p@\@minus\p@ + \parsep \z@ + \partopsep \p@ \@plus\z@ \@minus\p@} + +\renewcommand\labelitemi{\normalfont\bfseries --} +\renewcommand\labelitemii{$\m@th\bullet$} + +\setlength\arraycolsep{1.4\p@} +\setlength\tabcolsep{1.4\p@} + +\def\tableofcontents{\chapter*{\contentsname\@mkboth{{\contentsname}}% + {{\contentsname}}} + \def\authcount##1{\setcounter{auco}{##1}\setcounter{@auth}{1}} + \def\lastand{\ifnum\value{auco}=2\relax + \unskip{} \andname\ + \else + \unskip \lastandname\ + \fi}% + \def\and{\stepcounter{@auth}\relax + \ifnum\value{@auth}=\value{auco}% + \lastand + \else + \unskip, + \fi}% + \@starttoc{toc}\if@restonecol\twocolumn\fi} + +\def\l@part#1#2{\addpenalty{\@secpenalty}% + \addvspace{2em plus\p@}% % space above part line + \begingroup + \parindent \z@ + \rightskip \z@ plus 5em + \hrule\vskip5pt + \large % same size as for a contribution heading + \bfseries\boldmath % set line in boldface + \leavevmode % TeX command to enter horizontal mode. + #1\par + \vskip5pt + \hrule + \vskip1pt + \nobreak % Never break after part entry + \endgroup} + +\def\@dotsep{2} + +\let\phantomsection=\relax + +\def\hyperhrefextend{\ifx\hyper@anchor\@undefined\else +{}\fi} + +\def\addnumcontentsmark#1#2#3{% +\addtocontents{#1}{\protect\contentsline{#2}{\protect\numberline + {\thechapter}#3}{\thepage}\hyperhrefextend}}% +\def\addcontentsmark#1#2#3{% +\addtocontents{#1}{\protect\contentsline{#2}{#3}{\thepage}\hyperhrefextend}}% +\def\addcontentsmarkwop#1#2#3{% +\addtocontents{#1}{\protect\contentsline{#2}{#3}{0}\hyperhrefextend}}% + +\def\@adcmk[#1]{\ifcase #1 \or +\def\@gtempa{\addnumcontentsmark}% + \or \def\@gtempa{\addcontentsmark}% + \or \def\@gtempa{\addcontentsmarkwop}% + \fi\@gtempa{toc}{chapter}% +} +\def\addtocmark{% +\phantomsection +\@ifnextchar[{\@adcmk}{\@adcmk[3]}% +} + +\def\l@chapter#1#2{\addpenalty{-\@highpenalty} + \vskip 1.0em plus 1pt \@tempdima 1.5em \begingroup + \parindent \z@ \rightskip \@tocrmarg + \advance\rightskip by 0pt plus 2cm + \parfillskip -\rightskip \pretolerance=10000 + \leavevmode \advance\leftskip\@tempdima \hskip -\leftskip + {\large\bfseries\boldmath#1}\ifx0#2\hfil\null + \else + \nobreak + \leaders\hbox{$\m@th \mkern \@dotsep mu.\mkern + \@dotsep mu$}\hfill + \nobreak\hbox to\@pnumwidth{\hss #2}% + \fi\par + \penalty\@highpenalty \endgroup} + +\def\l@title#1#2{\addpenalty{-\@highpenalty} + \addvspace{8pt plus 1pt} + \@tempdima \z@ + \begingroup + \parindent \z@ \rightskip \@tocrmarg + \advance\rightskip by 0pt plus 2cm + \parfillskip -\rightskip \pretolerance=10000 + \leavevmode \advance\leftskip\@tempdima \hskip -\leftskip + #1\nobreak + \leaders\hbox{$\m@th \mkern \@dotsep mu.\mkern + \@dotsep mu$}\hfill + \nobreak\hbox to\@pnumwidth{\hss #2}\par + \penalty\@highpenalty \endgroup} + +\def\l@author#1#2{\addpenalty{\@highpenalty} + \@tempdima=15\p@ %\z@ + \begingroup + \parindent \z@ \rightskip \@tocrmarg + \advance\rightskip by 0pt plus 2cm + \pretolerance=10000 + \leavevmode \advance\leftskip\@tempdima %\hskip -\leftskip + \textit{#1}\par + \penalty\@highpenalty \endgroup} + +\setcounter{tocdepth}{0} +\newdimen\tocchpnum +\newdimen\tocsecnum +\newdimen\tocsectotal +\newdimen\tocsubsecnum +\newdimen\tocsubsectotal +\newdimen\tocsubsubsecnum +\newdimen\tocsubsubsectotal +\newdimen\tocparanum +\newdimen\tocparatotal +\newdimen\tocsubparanum +\tocchpnum=\z@ % no chapter numbers +\tocsecnum=15\p@ % section 88. plus 2.222pt +\tocsubsecnum=23\p@ % subsection 88.8 plus 2.222pt +\tocsubsubsecnum=27\p@ % subsubsection 88.8.8 plus 1.444pt +\tocparanum=35\p@ % paragraph 88.8.8.8 plus 1.666pt +\tocsubparanum=43\p@ % subparagraph 88.8.8.8.8 plus 1.888pt +\def\calctocindent{% +\tocsectotal=\tocchpnum +\advance\tocsectotal by\tocsecnum +\tocsubsectotal=\tocsectotal +\advance\tocsubsectotal by\tocsubsecnum +\tocsubsubsectotal=\tocsubsectotal +\advance\tocsubsubsectotal by\tocsubsubsecnum +\tocparatotal=\tocsubsubsectotal +\advance\tocparatotal by\tocparanum} +\calctocindent + +\def\l@section{\@dottedtocline{1}{\tocchpnum}{\tocsecnum}} +\def\l@subsection{\@dottedtocline{2}{\tocsectotal}{\tocsubsecnum}} +\def\l@subsubsection{\@dottedtocline{3}{\tocsubsectotal}{\tocsubsubsecnum}} +\def\l@paragraph{\@dottedtocline{4}{\tocsubsubsectotal}{\tocparanum}} +\def\l@subparagraph{\@dottedtocline{5}{\tocparatotal}{\tocsubparanum}} + +\def\listoffigures{\@restonecolfalse\if@twocolumn\@restonecoltrue\onecolumn + \fi\section*{\listfigurename\@mkboth{{\listfigurename}}{{\listfigurename}}} + \@starttoc{lof}\if@restonecol\twocolumn\fi} +\def\l@figure{\@dottedtocline{1}{0em}{1.5em}} + +\def\listoftables{\@restonecolfalse\if@twocolumn\@restonecoltrue\onecolumn + \fi\section*{\listtablename\@mkboth{{\listtablename}}{{\listtablename}}} + \@starttoc{lot}\if@restonecol\twocolumn\fi} +\let\l@table\l@figure + +\renewcommand\listoffigures{% + \section*{\listfigurename + \@mkboth{\listfigurename}{\listfigurename}}% + \@starttoc{lof}% + } + +\renewcommand\listoftables{% + \section*{\listtablename + \@mkboth{\listtablename}{\listtablename}}% + \@starttoc{lot}% + } + +\ifx\oribibl\undefined +\ifx\citeauthoryear\undefined +\renewenvironment{thebibliography}[1] + {\section*{\refname} + \def\@biblabel##1{##1.} + \small + \list{\@biblabel{\@arabic\c@enumiv}}% + {\settowidth\labelwidth{\@biblabel{#1}}% + \leftmargin\labelwidth + \advance\leftmargin\labelsep + \if@openbib + \advance\leftmargin\bibindent + \itemindent -\bibindent + \listparindent \itemindent + \parsep \z@ + \fi + \usecounter{enumiv}% + \let\p@enumiv\@empty + \renewcommand\theenumiv{\@arabic\c@enumiv}}% + \if@openbib + \renewcommand\newblock{\par}% + \else + \renewcommand\newblock{\hskip .11em \@plus.33em \@minus.07em}% + \fi + \sloppy\clubpenalty4000\widowpenalty4000% + \sfcode`\.=\@m} + {\def\@noitemerr + {\@latex@warning{Empty `thebibliography' environment}}% + \endlist} +\def\@lbibitem[#1]#2{\item[{[#1]}\hfill]\if@filesw + {\let\protect\noexpand\immediate + \write\@auxout{\string\bibcite{#2}{#1}}}\fi\ignorespaces} +\newcount\@tempcntc +\def\@citex[#1]#2{\if@filesw\immediate\write\@auxout{\string\citation{#2}}\fi + \@tempcnta\z@\@tempcntb\m@ne\def\@citea{}\@cite{\@for\@citeb:=#2\do + {\@ifundefined + {b@\@citeb}{\@citeo\@tempcntb\m@ne\@citea\def\@citea{,}{\bfseries + ?}\@warning + {Citation `\@citeb' on page \thepage \space undefined}}% + {\setbox\z@\hbox{\global\@tempcntc0\csname b@\@citeb\endcsname\relax}% + \ifnum\@tempcntc=\z@ \@citeo\@tempcntb\m@ne + \@citea\def\@citea{,}\hbox{\csname b@\@citeb\endcsname}% + \else + \advance\@tempcntb\@ne + \ifnum\@tempcntb=\@tempcntc + \else\advance\@tempcntb\m@ne\@citeo + \@tempcnta\@tempcntc\@tempcntb\@tempcntc\fi\fi}}\@citeo}{#1}} +\def\@citeo{\ifnum\@tempcnta>\@tempcntb\else + \@citea\def\@citea{,\,\hskip\z@skip}% + \ifnum\@tempcnta=\@tempcntb\the\@tempcnta\else + {\advance\@tempcnta\@ne\ifnum\@tempcnta=\@tempcntb \else + \def\@citea{--}\fi + \advance\@tempcnta\m@ne\the\@tempcnta\@citea\the\@tempcntb}\fi\fi} +\else +\renewenvironment{thebibliography}[1] + {\section*{\refname} + \small + \list{}% + {\settowidth\labelwidth{}% + \leftmargin\parindent + \itemindent=-\parindent + \labelsep=\z@ + \if@openbib + \advance\leftmargin\bibindent + \itemindent -\bibindent + \listparindent \itemindent + \parsep \z@ + \fi + \usecounter{enumiv}% + \let\p@enumiv\@empty + \renewcommand\theenumiv{}}% + \if@openbib + \renewcommand\newblock{\par}% + \else + \renewcommand\newblock{\hskip .11em \@plus.33em \@minus.07em}% + \fi + \sloppy\clubpenalty4000\widowpenalty4000% + \sfcode`\.=\@m} + {\def\@noitemerr + {\@latex@warning{Empty `thebibliography' environment}}% + \endlist} + \def\@cite#1{#1}% + \def\@lbibitem[#1]#2{\item[]\if@filesw + {\def\protect##1{\string ##1\space}\immediate + \write\@auxout{\string\bibcite{#2}{#1}}}\fi\ignorespaces} + \fi +\else +\@cons\@openbib@code{\noexpand\small} +\fi + +\def\idxquad{\hskip 10\p@}% space that divides entry from number + +\def\@idxitem{\par\hangindent 10\p@} + +\def\subitem{\par\setbox0=\hbox{--\enspace}% second order + \noindent\hangindent\wd0\box0}% index entry + +\def\subsubitem{\par\setbox0=\hbox{--\,--\enspace}% third + \noindent\hangindent\wd0\box0}% order index entry + +\def\indexspace{\par \vskip 10\p@ plus5\p@ minus3\p@\relax} + +\renewenvironment{theindex} + {\@mkboth{\indexname}{\indexname}% + \thispagestyle{empty}\parindent\z@ + \parskip\z@ \@plus .3\p@\relax + \let\item\par + \def\,{\relax\ifmmode\mskip\thinmuskip + \else\hskip0.2em\ignorespaces\fi}% + \normalfont\small + \begin{multicols}{2}[\@makeschapterhead{\indexname}]% + } + {\end{multicols}} + +\renewcommand\footnoterule{% + \kern-3\p@ + \hrule\@width 2truecm + \kern2.6\p@} + \newdimen\fnindent + \fnindent1em +\long\def\@makefntext#1{% + \parindent \fnindent% + \leftskip \fnindent% + \noindent + \llap{\hb@xt@1em{\hss\@makefnmark\ }}\ignorespaces#1} + +\long\def\@makecaption#1#2{% + \small + \vskip\abovecaptionskip + \sbox\@tempboxa{{\bfseries #1.} #2}% + \ifdim \wd\@tempboxa >\hsize + {\bfseries #1.} #2\par + \else + \global \@minipagefalse + \hb@xt@\hsize{\hfil\box\@tempboxa\hfil}% + \fi + \vskip\belowcaptionskip} + +\def\fps@figure{htbp} +\def\fnum@figure{\figurename\thinspace\thefigure} +\def \@floatboxreset {% + \reset@font + \small + \@setnobreak + \@setminipage +} +\def\fps@table{htbp} +\def\fnum@table{\tablename~\thetable} +\renewenvironment{table} + {\setlength\abovecaptionskip{0\p@}% + \setlength\belowcaptionskip{10\p@}% + \@float{table}} + {\end@float} +\renewenvironment{table*} + {\setlength\abovecaptionskip{0\p@}% + \setlength\belowcaptionskip{10\p@}% + \@dblfloat{table}} + {\end@dblfloat} + +\long\def\@caption#1[#2]#3{\par\addcontentsline{\csname + ext@#1\endcsname}{#1}{\protect\numberline{\csname + the#1\endcsname}{\ignorespaces #2}}\begingroup + \@parboxrestore + \@makecaption{\csname fnum@#1\endcsname}{\ignorespaces #3}\par + \endgroup} + +% LaTeX does not provide a command to enter the authors institute +% addresses. The \institute command is defined here. + +\newcounter{@inst} +\newcounter{@auth} +\newcounter{auco} +\newdimen\instindent +\newbox\authrun +\newtoks\authorrunning +\newtoks\tocauthor +\newbox\titrun +\newtoks\titlerunning +\newtoks\toctitle + +\def\clearheadinfo{\gdef\@author{No Author Given}% + \gdef\@title{No Title Given}% + \gdef\@subtitle{}% + \gdef\@institute{No Institute Given}% + \gdef\@thanks{}% + \global\titlerunning={}\global\authorrunning={}% + \global\toctitle={}\global\tocauthor={}} + +\def\institute#1{\gdef\@institute{#1}} + +\def\institutename{\par + \begingroup + \parskip=\z@ + \parindent=\z@ + \setcounter{@inst}{1}% + \def\and{\par\stepcounter{@inst}% + \noindent$^{\the@inst}$\enspace\ignorespaces}% + \setbox0=\vbox{\def\thanks##1{}\@institute}% + \ifnum\c@@inst=1\relax + \gdef\fnnstart{0}% + \else + \xdef\fnnstart{\c@@inst}% + \setcounter{@inst}{1}% + \noindent$^{\the@inst}$\enspace + \fi + \ignorespaces + \@institute\par + \endgroup} + +\def\@fnsymbol#1{\ensuremath{\ifcase#1\or\star\or{\star\star}\or + {\star\star\star}\or \dagger\or \ddagger\or + \mathchar "278\or \mathchar "27B\or \|\or **\or \dagger\dagger + \or \ddagger\ddagger \else\@ctrerr\fi}} + +\def\inst#1{\unskip$^{#1}$} +\def\fnmsep{\unskip$^,$} +\def\email#1{{\tt#1}} +\AtBeginDocument{\@ifundefined{url}{\def\url#1{#1}}{}% +\@ifpackageloaded{babel}{% +\@ifundefined{extrasenglish}{}{\addto\extrasenglish{\switcht@albion}}% +\@ifundefined{extrasfrenchb}{}{\addto\extrasfrenchb{\switcht@francais}}% +\@ifundefined{extrasgerman}{}{\addto\extrasgerman{\switcht@deutsch}}% +}{\switcht@@therlang}% +\providecommand{\keywords}[1]{\par\addvspace\baselineskip +\noindent\keywordname\enspace\ignorespaces#1}% +} +\def\homedir{\~{ }} + +\def\subtitle#1{\gdef\@subtitle{#1}} +\clearheadinfo +% +%%% to avoid hyperref warnings +\providecommand*{\toclevel@author}{999} +%%% to make title-entry parent of section-entries +\providecommand*{\toclevel@title}{0} +% +\renewcommand\maketitle{\newpage +\phantomsection + \refstepcounter{chapter}% + \stepcounter{section}% + \setcounter{section}{0}% + \setcounter{subsection}{0}% + \setcounter{figure}{0} + \setcounter{table}{0} + \setcounter{equation}{0} + \setcounter{footnote}{0}% + \begingroup + \parindent=\z@ + \renewcommand\thefootnote{\@fnsymbol\c@footnote}% + \if@twocolumn + \ifnum \col@number=\@ne + \@maketitle + \else + \twocolumn[\@maketitle]% + \fi + \else + \newpage + \global\@topnum\z@ % Prevents figures from going at top of page. + \@maketitle + \fi + \thispagestyle{empty}\@thanks +% + \def\\{\unskip\ \ignorespaces}\def\inst##1{\unskip{}}% + \def\thanks##1{\unskip{}}\def\fnmsep{\unskip}% + \instindent=\hsize + \advance\instindent by-\headlineindent + \if!\the\toctitle!\addcontentsline{toc}{title}{\@title}\else + \addcontentsline{toc}{title}{\the\toctitle}\fi + \if@runhead + \if!\the\titlerunning!\else + \edef\@title{\the\titlerunning}% + \fi + \global\setbox\titrun=\hbox{\small\rm\unboldmath\ignorespaces\@title}% + \ifdim\wd\titrun>\instindent + \typeout{Title too long for running head. Please supply}% + \typeout{a shorter form with \string\titlerunning\space prior to + \string\maketitle}% + \global\setbox\titrun=\hbox{\small\rm + Title Suppressed Due to Excessive Length}% + \fi + \xdef\@title{\copy\titrun}% + \fi +% + \if!\the\tocauthor!\relax + {\def\and{\noexpand\protect\noexpand\and}% + \protected@xdef\toc@uthor{\@author}}% + \else + \def\\{\noexpand\protect\noexpand\newline}% + \protected@xdef\scratch{\the\tocauthor}% + \protected@xdef\toc@uthor{\scratch}% + \fi + \addtocontents{toc}{\noexpand\protect\noexpand\authcount{\the\c@auco}}% + \addcontentsline{toc}{author}{\toc@uthor}% + \if@runhead + \if!\the\authorrunning! + \value{@inst}=\value{@auth}% + \setcounter{@auth}{1}% + \else + \edef\@author{\the\authorrunning}% + \fi + \global\setbox\authrun=\hbox{\small\unboldmath\@author\unskip}% + \ifdim\wd\authrun>\instindent + \typeout{Names of authors too long for running head. Please supply}% + \typeout{a shorter form with \string\authorrunning\space prior to + \string\maketitle}% + \global\setbox\authrun=\hbox{\small\rm + Authors Suppressed Due to Excessive Length}% + \fi + \xdef\@author{\copy\authrun}% + \markboth{\@author}{\@title}% + \fi + \endgroup + \setcounter{footnote}{\fnnstart}% + \clearheadinfo} +% +\def\@maketitle{\newpage + \markboth{}{}% + \def\lastand{\ifnum\value{@inst}=2\relax + \unskip{} \andname\ + \else + \unskip \lastandname\ + \fi}% + \def\and{\stepcounter{@auth}\relax + \ifnum\value{@auth}=\value{@inst}% + \lastand + \else + \unskip, + \fi}% + \begin{center}% + \let\newline\\ + {\Large \bfseries\boldmath + \pretolerance=10000 + \@title \par}\vskip .8cm +\if!\@subtitle!\else {\large \bfseries\boldmath + \vskip -.65cm + \pretolerance=10000 + \@subtitle \par}\vskip .8cm\fi + \setbox0=\vbox{\setcounter{@auth}{1}\def\and{\stepcounter{@auth}}% + \def\thanks##1{}\@author}% + \global\value{@inst}=\value{@auth}% + \global\value{auco}=\value{@auth}% + \setcounter{@auth}{1}% +{\lineskip .5em +\noindent\ignorespaces +\@author\vskip.35cm} + {\small\institutename} + \end{center}% + } + +% definition of the "\spnewtheorem" command. +% +% Usage: +% +% \spnewtheorem{env_nam}{caption}[within]{cap_font}{body_font} +% or \spnewtheorem{env_nam}[numbered_like]{caption}{cap_font}{body_font} +% or \spnewtheorem*{env_nam}{caption}{cap_font}{body_font} +% +% New is "cap_font" and "body_font". It stands for +% fontdefinition of the caption and the text itself. +% +% "\spnewtheorem*" gives a theorem without number. +% +% A defined spnewthoerem environment is used as described +% by Lamport. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\def\@thmcountersep{} +\def\@thmcounterend{.} + +\def\spnewtheorem{\@ifstar{\@sthm}{\@Sthm}} + +% definition of \spnewtheorem with number + +\def\@spnthm#1#2{% + \@ifnextchar[{\@spxnthm{#1}{#2}}{\@spynthm{#1}{#2}}} +\def\@Sthm#1{\@ifnextchar[{\@spothm{#1}}{\@spnthm{#1}}} + +\def\@spxnthm#1#2[#3]#4#5{\expandafter\@ifdefinable\csname #1\endcsname + {\@definecounter{#1}\@addtoreset{#1}{#3}% + \expandafter\xdef\csname the#1\endcsname{\expandafter\noexpand + \csname the#3\endcsname \noexpand\@thmcountersep \@thmcounter{#1}}% + \expandafter\xdef\csname #1name\endcsname{#2}% + \global\@namedef{#1}{\@spthm{#1}{\csname #1name\endcsname}{#4}{#5}}% + \global\@namedef{end#1}{\@endtheorem}}} + +\def\@spynthm#1#2#3#4{\expandafter\@ifdefinable\csname #1\endcsname + {\@definecounter{#1}% + \expandafter\xdef\csname the#1\endcsname{\@thmcounter{#1}}% + \expandafter\xdef\csname #1name\endcsname{#2}% + \global\@namedef{#1}{\@spthm{#1}{\csname #1name\endcsname}{#3}{#4}}% + \global\@namedef{end#1}{\@endtheorem}}} + +\def\@spothm#1[#2]#3#4#5{% + \@ifundefined{c@#2}{\@latexerr{No theorem environment `#2' defined}\@eha}% + {\expandafter\@ifdefinable\csname #1\endcsname + {\newaliascnt{#1}{#2}% + \expandafter\xdef\csname #1name\endcsname{#3}% + \global\@namedef{#1}{\@spthm{#1}{\csname #1name\endcsname}{#4}{#5}}% + \global\@namedef{end#1}{\@endtheorem}}}} + +\def\@spthm#1#2#3#4{\topsep 7\p@ \@plus2\p@ \@minus4\p@ +\refstepcounter{#1}% +\@ifnextchar[{\@spythm{#1}{#2}{#3}{#4}}{\@spxthm{#1}{#2}{#3}{#4}}} + +\def\@spxthm#1#2#3#4{\@spbegintheorem{#2}{\csname the#1\endcsname}{#3}{#4}% + \ignorespaces} + +\def\@spythm#1#2#3#4[#5]{\@spopargbegintheorem{#2}{\csname + the#1\endcsname}{#5}{#3}{#4}\ignorespaces} + +\def\@spbegintheorem#1#2#3#4{\trivlist + \item[\hskip\labelsep{#3#1\ #2\@thmcounterend}]#4} + +\def\@spopargbegintheorem#1#2#3#4#5{\trivlist + \item[\hskip\labelsep{#4#1\ #2}]{#4(#3)\@thmcounterend\ }#5} + +% definition of \spnewtheorem* without number + +\def\@sthm#1#2{\@Ynthm{#1}{#2}} + +\def\@Ynthm#1#2#3#4{\expandafter\@ifdefinable\csname #1\endcsname + {\global\@namedef{#1}{\@Thm{\csname #1name\endcsname}{#3}{#4}}% + \expandafter\xdef\csname #1name\endcsname{#2}% + \global\@namedef{end#1}{\@endtheorem}}} + +\def\@Thm#1#2#3{\topsep 7\p@ \@plus2\p@ \@minus4\p@ +\@ifnextchar[{\@Ythm{#1}{#2}{#3}}{\@Xthm{#1}{#2}{#3}}} + +\def\@Xthm#1#2#3{\@Begintheorem{#1}{#2}{#3}\ignorespaces} + +\def\@Ythm#1#2#3[#4]{\@Opargbegintheorem{#1} + {#4}{#2}{#3}\ignorespaces} + +\def\@Begintheorem#1#2#3{#3\trivlist + \item[\hskip\labelsep{#2#1\@thmcounterend}]} + +\def\@Opargbegintheorem#1#2#3#4{#4\trivlist + \item[\hskip\labelsep{#3#1}]{#3(#2)\@thmcounterend\ }} + +\if@envcntsect + \def\@thmcountersep{.} + \spnewtheorem{theorem}{Theorem}[section]{\bfseries}{\itshape} +\else + \spnewtheorem{theorem}{Theorem}{\bfseries}{\itshape} + \if@envcntreset + \@addtoreset{theorem}{section} + \else + \@addtoreset{theorem}{chapter} + \fi +\fi + +%definition of divers theorem environments +\spnewtheorem*{claim}{Claim}{\itshape}{\rmfamily} +\spnewtheorem*{proof}{Proof}{\itshape}{\rmfamily} +\if@envcntsame % alle Umgebungen wie Theorem. + \def\spn@wtheorem#1#2#3#4{\@spothm{#1}[theorem]{#2}{#3}{#4}} +\else % alle Umgebungen mit eigenem Zaehler + \if@envcntsect % mit section numeriert + \def\spn@wtheorem#1#2#3#4{\@spxnthm{#1}{#2}[section]{#3}{#4}} + \else % nicht mit section numeriert + \if@envcntreset + \def\spn@wtheorem#1#2#3#4{\@spynthm{#1}{#2}{#3}{#4} + \@addtoreset{#1}{section}} + \else + \def\spn@wtheorem#1#2#3#4{\@spynthm{#1}{#2}{#3}{#4} + \@addtoreset{#1}{chapter}}% + \fi + \fi +\fi +\spn@wtheorem{case}{Case}{\itshape}{\rmfamily} +\spn@wtheorem{conjecture}{Conjecture}{\itshape}{\rmfamily} +\spn@wtheorem{corollary}{Corollary}{\bfseries}{\itshape} +\spn@wtheorem{definition}{Definition}{\bfseries}{\itshape} +\spn@wtheorem{example}{Example}{\itshape}{\rmfamily} +\spn@wtheorem{exercise}{Exercise}{\itshape}{\rmfamily} +\spn@wtheorem{lemma}{Lemma}{\bfseries}{\itshape} +\spn@wtheorem{note}{Note}{\itshape}{\rmfamily} +\spn@wtheorem{problem}{Problem}{\itshape}{\rmfamily} +\spn@wtheorem{property}{Property}{\itshape}{\rmfamily} +\spn@wtheorem{proposition}{Proposition}{\bfseries}{\itshape} +\spn@wtheorem{question}{Question}{\itshape}{\rmfamily} +\spn@wtheorem{solution}{Solution}{\itshape}{\rmfamily} +\spn@wtheorem{remark}{Remark}{\itshape}{\rmfamily} + +\def\@takefromreset#1#2{% + \def\@tempa{#1}% + \let\@tempd\@elt + \def\@elt##1{% + \def\@tempb{##1}% + \ifx\@tempa\@tempb\else + \@addtoreset{##1}{#2}% + \fi}% + \expandafter\expandafter\let\expandafter\@tempc\csname cl@#2\endcsname + \expandafter\def\csname cl@#2\endcsname{}% + \@tempc + \let\@elt\@tempd} + +\def\theopargself{\def\@spopargbegintheorem##1##2##3##4##5{\trivlist + \item[\hskip\labelsep{##4##1\ ##2}]{##4##3\@thmcounterend\ }##5} + \def\@Opargbegintheorem##1##2##3##4{##4\trivlist + \item[\hskip\labelsep{##3##1}]{##3##2\@thmcounterend\ }} + } + +\renewenvironment{abstract}{% + \list{}{\advance\topsep by0.35cm\relax\small + \leftmargin=1cm + \labelwidth=\z@ + \listparindent=\z@ + \itemindent\listparindent + \rightmargin\leftmargin}\item[\hskip\labelsep + \bfseries\abstractname]} + {\endlist} + +\newdimen\headlineindent % dimension for space between +\headlineindent=1.166cm % number and text of headings. + +\def\ps@headings{\let\@mkboth\@gobbletwo + \let\@oddfoot\@empty\let\@evenfoot\@empty + \def\@evenhead{\normalfont\small\rlap{\thepage}\hspace{\headlineindent}% + \leftmark\hfil} + \def\@oddhead{\normalfont\small\hfil\rightmark\hspace{\headlineindent}% + \llap{\thepage}} + \def\chaptermark##1{}% + \def\sectionmark##1{}% + \def\subsectionmark##1{}} + +\def\ps@titlepage{\let\@mkboth\@gobbletwo + \let\@oddfoot\@empty\let\@evenfoot\@empty + \def\@evenhead{\normalfont\small\rlap{\thepage}\hspace{\headlineindent}% + \hfil} + \def\@oddhead{\normalfont\small\hfil\hspace{\headlineindent}% + \llap{\thepage}} + \def\chaptermark##1{}% + \def\sectionmark##1{}% + \def\subsectionmark##1{}} + +\if@runhead\ps@headings\else +\ps@empty\fi + +\setlength\arraycolsep{1.4\p@} +\setlength\tabcolsep{1.4\p@} + +\endinput +%end of file llncs.cls diff --git a/crCOUCHOT14/main.aux b/crCOUCHOT14/main.aux new file mode 100644 index 0000000..b0d42dc --- /dev/null +++ b/crCOUCHOT14/main.aux @@ -0,0 +1,41 @@ +\relax +\citation{Nist10} +\citation{Marsaglia1996} +\citation{BCGR11} +\select@language{english} +\@writefile{toc}{\select@language{english}} +\@writefile{lof}{\select@language{english}} +\@writefile{lot}{\select@language{english}} +\newlabel{sec:preliminaries}{{2}{2}} +\newlabel{eq:asyn}{{1}{2}} +\providecommand*\caption@xref[2]{\@setref\relax\@undefined{#1}} +\newlabel{fig:iteration:f*}{{1}{2}} +\citation{BCGR11} +\citation{BCGR11} +\citation{BCGR11} +\newlabel{CI Algorithm}{{1}{3}} +\newlabel{sec:DSSC}{{3}{3}} +\newlabel{table:mixing:3}{{1}{3}} +\citation{journals/combinatorics/BhatS96,VanSup04,journals/combinatorics/FlahiveB07} +\citation{Feder:2009:NTB:1496397.1496515} +\newlabel{sec:hamiltonian}{{4}{4}} +\newlabel{sub:gray}{{4.2}{4}} +\citation{VanSup04} +\citation{VanSup04} +\newlabel{sub:algo:gray}{{4.3}{5}} +\newlabel{item:nondet}{{1}{5}} +\newlabel{table:combinations}{{2}{5}} +\newlabel{table:nbFunc}{{3}{5}} +\newlabel{sec:exp}{{5}{5}} +\bibstyle{apalike} +\bibdata{markov} +\bibcite{BCGR11}{Bahi et~al., 2011} +\bibcite{Nist10}{Barker and Roginsky, 2010} +\bibcite{journals/combinatorics/BhatS96}{Bhat and Savage, 1996} +\bibcite{Feder:2009:NTB:1496397.1496515}{Feder and Subi, 2009} +\bibcite{journals/combinatorics/FlahiveB07}{Flahive and Bose, 2007} +\bibcite{Marsaglia1996}{Marsaglia, 1996} +\bibcite{VanSup04}{Zanten and Suparta, 2004} +\newlabel{table:nc}{{4}{6}} +\newlabel{The passing rate}{{5}{6}} +\newlabel{sec:conclusion}{{6}{6}} diff --git a/crCOUCHOT14/main.bbl b/crCOUCHOT14/main.bbl new file mode 100644 index 0000000..cb9ff2d --- /dev/null +++ b/crCOUCHOT14/main.bbl @@ -0,0 +1,42 @@ +\begin{thebibliography}{} + +\bibitem[Bahi et~al., 2011]{BCGR11} +Bahi, J., Couchot, J.-F., Guyeux, C., and Richard, A. (2011). +\newblock On the link between strongly connected iteration graphs and chaotic + boolean discrete-time dynamical systems. +\newblock In Owe, O., Steffen, M., and Telle, J., editors, {\em Fundamentals of + Computation Theory}, volume 6914 of {\em Lecture Notes in Computer Science}, + pages 126--137. Springer Berlin Heidelberg. + +\bibitem[Barker and Roginsky, 2010]{Nist10} +Barker, E. and Roginsky, A. (2010). +\newblock Draft {N}{I}{S}{T} special publication 800-131 recommendation for the + transitioning of cryptographic algorithms and key sizes. + +\bibitem[Bhat and Savage, 1996]{journals/combinatorics/BhatS96} +Bhat, G.~S. and Savage, C.~D. (1996). +\newblock Balanced gray codes. +\newblock {\em Electr. J. Comb.}, 3(1). + +\bibitem[Feder and Subi, 2009]{Feder:2009:NTB:1496397.1496515} +Feder, T. and Subi, C. (2009). +\newblock Nearly tight bounds on the number of hamiltonian circuits of the + hypercube and generalizations. +\newblock {\em Inf. Process. Lett.}, 109(5):267--272. + +\bibitem[Flahive and Bose, 2007]{journals/combinatorics/FlahiveB07} +Flahive, M. and Bose, B. (2007). +\newblock Balancing cyclic r-ary gray codes. +\newblock {\em Electr. J. Comb.}, 14(1). + +\bibitem[Marsaglia, 1996]{Marsaglia1996} +Marsaglia, G. (1996). +\newblock Die{HARD}: a battery of tests of randomness. +\newblock {\em http://stat.fsu.edu/~geo/diehard.html}. + +\bibitem[Zanten and Suparta, 2004]{VanSup04} +Zanten, A.~J.~v. and Suparta, I.~N. (2004). +\newblock Totally balanced and exponentially balanced gray codes. +\newblock {\em Discrete Analysis and Operational Research}, 11:81--98. + +\end{thebibliography} diff --git a/crCOUCHOT14/main.blg b/crCOUCHOT14/main.blg new file mode 100644 index 0000000..b39c8cc --- /dev/null +++ b/crCOUCHOT14/main.blg @@ -0,0 +1,46 @@ +This is BibTeX, Version 0.99d (TeX Live 2013/Debian) +Capacity: max_strings=35307, hash_size=35307, hash_prime=30011 +The top-level auxiliary file: main.aux +The style file: apalike.bst +Database file #1: markov.bib +You've used 7 entries, + 1935 wiz_defined-function locations, + 524 strings with 5040 characters, +and the built_in function-call counts, 2645 in all, are: += -- 259 +> -- 106 +< -- 8 ++ -- 33 +- -- 33 +* -- 219 +:= -- 467 +add.period$ -- 21 +call.type$ -- 7 +change.case$ -- 50 +chr.to.int$ -- 7 +cite$ -- 7 +duplicate$ -- 105 +empty$ -- 181 +format.name$ -- 50 +if$ -- 520 +int.to.chr$ -- 1 +int.to.str$ -- 0 +missing$ -- 6 +newline$ -- 37 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U+dsrom on input line 175. + + +(/usr/share/texlive/texmf-dist/tex/latex/doublestroke/Udsrom.fd +File: Udsrom.fd 1995/08/01 v0.1 Double stroke roman font definitions +) +LaTeX Font Info: Font shape `T1/ptm/bx/n' in size <10> not available +(Font) Font shape `T1/ptm/b/n' tried instead on input line 207. +Package epstopdf Info: Source file: +(epstopdf) date: 2014-07-02 17:09:12 +(epstopdf) size: 13736 bytes +(epstopdf) Output file: +(epstopdf) date: 2014-07-02 17:09:12 +(epstopdf) size: 4752 bytes +(epstopdf) Command: +(epstopdf) \includegraphics on input line 216. +Package epstopdf Info: Output file is already uptodate. + + +File: iter_f0b-eps-converted-to.pdf Graphic file (type pdf) + + +Package pdftex.def Info: iter_f0b-eps-converted-to.pdf used on input line 216. +(pdftex.def) Requested size: 175.15395pt x 130.48718pt. + [2 <./iter_f0b-eps-converted-to.pdf>] +LaTeX Font Info: Font shape `T1/ptm/bx/n' in size <12> not available +(Font) Font shape `T1/ptm/b/n' tried instead on input line 345. + +Underfull \hbox (badness 2213) in paragraph at lines 360--362 +[]\T1/ptm/m/n/10 For any in-dex of line $\OML/ptmcm/m/it/10 i$\T1/ptm/m/n/10 , +$\OT1/ptmcm/m/n/10 1 \OMS/pzccm/m/n/10 ^^T \OML/ptmcm/m/it/10 i \OMS/pzccm/m/n/ +10 ^^T \OT1/ptmcm/m/n/10 2[]$\T1/ptm/m/n/10 , $\OML/ptmcm/m/it/10 n \OT1/ptmcm/ +m/n/10 = + [] + + +Underfull \hbox (badness 2875) in paragraph at lines 434--446 +\T1/ptm/m/n/10 the cy-cle $\OT1/ptmcm/m/n/10 000\OML/ptmcm/m/it/10 ; \OT1/ptmcm +/m/n/10 100\OML/ptmcm/m/it/10 ; \OT1/ptmcm/m/n/10 101\OML/ptmcm/m/it/10 ; \OT1/ +ptmcm/m/n/10 001\OML/ptmcm/m/it/10 ; \OT1/ptmcm/m/n/10 011\OML/ptmcm/m/it/10 ; +\OT1/ptmcm/m/n/10 111\OML/ptmcm/m/it/10 ; \OT1/ptmcm/m/n/10 110\OML/ptmcm/m/it/ +10 ; \OT1/ptmcm/m/n/10 010\OML/ptmcm/m/it/10 ; \OT1/ptmcm/m/n/10 000$ + [] + +[3] +Underfull \hbox (badness 4144) in paragraph at lines 544--549 +[]\T1/ptm/b/n/10 Running ex-am-ple. []\T1/ptm/m/it/10 Let $\OML/ptmcm/m/it/10 L +[]$ \T1/ptm/m/it/10 be the Gray code + [] + + +Underfull \hbox (badness 10000) in paragraph at lines 544--549 +\OT1/ptmcm/m/n/10 000\OML/ptmcm/m/it/10 ; \OT1/ptmcm/m/n/10 100\OML/ptmcm/m/it/ +10 ; \OT1/ptmcm/m/n/10 101\OML/ptmcm/m/it/10 ; \OT1/ptmcm/m/n/10 001\OML/ptmcm/ +m/it/10 ; \OT1/ptmcm/m/n/10 011\OML/ptmcm/m/it/10 ; \OT1/ptmcm/m/n/10 111\OML/p +tmcm/m/it/10 ; \OT1/ptmcm/m/n/10 110\OML/ptmcm/m/it/10 ; \OT1/ptmcm/m/n/10 010$ + \T1/ptm/m/it/10 that cor-re- + [] + + +Underfull \hbox (badness 2035) in paragraph at lines 544--549 +\T1/ptm/m/it/10 sponds to the Hamil-to-nian cy-cle that has been + [] + + +Underfull \hbox (badness 1412) in paragraph at lines 544--549 +\T1/ptm/m/it/10 se-quence is $\OML/ptmcm/m/it/10 S \OT1/ptmcm/m/n/10 = 3\OML/pt +mcm/m/it/10 ; \OT1/ptmcm/m/n/10 1\OML/ptmcm/m/it/10 ; \OT1/ptmcm/m/n/10 3\OML/p +tmcm/m/it/10 ; \OT1/ptmcm/m/n/10 2\OML/ptmcm/m/it/10 ; \OT1/ptmcm/m/n/10 3\OML/ +ptmcm/m/it/10 ; \OT1/ptmcm/m/n/10 1\OML/ptmcm/m/it/10 ; \OT1/ptmcm/m/n/10 3\OML +/ptmcm/m/it/10 ; \OT1/ptmcm/m/n/10 2$ \T1/ptm/m/it/10 and its tran-si- + [] + + +Underfull \hbox (badness 10000) in paragraph at lines 550--555 +[]\T1/ptm/m/it/10 Let $\OML/ptmcm/m/it/10 L[]$ \T1/ptm/m/it/10 be the cyclic Gr +ay code + [] + + +Underfull \hbox (badness 10000) in paragraph at lines 550--555 +\OT1/ptmcm/m/n/10 0100\OML/ptmcm/m/it/10 ; \OT1/ptmcm/m/n/10 1100\OML/ptmcm/m/i +t/10 ; \OT1/ptmcm/m/n/10 1101\OML/ptmcm/m/it/10 ; \OT1/ptmcm/m/n/10 1001\OML/pt +mcm/m/it/10 ; \OT1/ptmcm/m/n/10 1011\OML/ptmcm/m/it/10 ; \OT1/ptmcm/m/n/10 1010 +\OML/ptmcm/m/it/10 ; \OT1/ptmcm/m/n/10 1000$\T1/ptm/m/it/10 . Since + [] + +[4] +Underfull \hbox (badness 4254) in paragraph at lines 567--570 +[]\T1/ptm/m/n/10 Let $\OML/ptmcm/m/it/10 l$ \T1/ptm/m/n/10 be an even pos-i-tiv +e in-te-ger. 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Couchot\sup{1}, P.-C. Heam\sup{1}, C. Guyeux\sup{1}, Q. Wang\sup{2}, and J. M. Bahi\sup{1}} +\affiliation{\sup{1}FEMTO-ST Institute, University of Franche-Comt\'{e}, France} +\affiliation{\sup{2}College of Automation, Guangdong University of Technology, China } +\email{\{jean-francois.couchot,pierre-cyrille.heam,christophe.guyeux,jacques.bahi\}@univ-fcomte.fr, wangqianxue@gdut.edu.cn} +} + +\keywords{Pseudorandom Number Generator, Theory of Chaos, Markov Matrices, Hamiltonian Paths, Mixing Time, Gray Codes, Statistical Tests} + +\abstract{In this article, +it is shown that a large class of truly chaotic Pseudorandom Number Generators +can be constructed. The generators are based on iterating Boolean maps, which are computed +using balanced Gray codes. The number of such Gray codes gives the size of the class. +The construction of such generators is automatic for small number of bits, but remains an open problem when this +number becomes large. A running example is used throughout the paper. Finally, first statistical experiments of these generators are presented, they show how efficient and promising the proposed +approach seems.} + + +\onecolumn \maketitle \normalsize \vfill + + + + + + +\vspace{-8em} +\section{\uppercase{Introduction}} +\vspace{-1em} +Many fields of research or applications like numerical simulations, +stochastic optimization, or information security are highly dependent on +the use of fast and unbiased random number generators. Depending on the +targeted application, reproducibility must be either required, leading +to deterministic algorithms that produce numbers as close as possible +to random sequences, or refused, which implies to use an external +physical noise. The formers are called pseudorandom number generators +(PRNGs) while the laters are designed by truly random number generators (TRNGs). +TRNGs are used for instance in cypher keys generation, or in hardware based +simulations or security devices. Such TRNGs are often based on a chaotic +physical signal, may be quantized depending on the application. +This quantization however raises the problem of the degradation of chaotic +properties. + +The use of PRNGs, for its part, is a necessity in a large variety +of numerical simulations, in which +responses of devices under study must be compared using the same ``random'' +stream. This reproducibility is required too for symmetric encryption like +one-time pad, as sender and receiver must share the same pad. However, in +that situation, security of the pseudorandom stream must be mathematically +proven: an attacker must not be able to computationally distinguish a +pseudorandom sequence generated by the considered PRNG with a really random +one. Such cryptographically secure pseudorandom number generators are +however only useful in cryptographic contexts, due to their slowness +resulting from their security. + + +Other kind of properties are desired for PRNGs used in numerical simulations +or in programs that embed a Monte-Carlo algorithm. In these situations, +required properties are speed and random-like profiles of the generated +sequences. The fact that a given PRNG is unbiased and behaves as a white +noise is thus verified using batteries of statistical tests on a large amount +of pseudorandom numbers. Reputed and up-to-date batteries are +currently the NIST suite~\cite{Nist10}, and DieHARD~\cite{Marsaglia1996}. +%and TestU01~\cite{Simard07testu01:a}, this latter being the +%most stringent one. +Finally, chaotic properties can be desired when +simulating a chaotic physical phenomenon or in hardware security, in +which cryptographical proofs are not realizable. +In both truly and pseudorandom number generation, there is thus a need +to mathematically guarantee the presence of chaos, and to show that +a post-treatment on a given secure and/or unbiased generator can be realized, +which adds chaos without deflating these desired properties. + + +This work takes place in this domain with the desire of automatically +generating a large class of PRNGs with chaos and statistical properties. +In a sense, it is close to~\cite{BCGR11} where the authors shown that +some Boolean maps may be embedded into an algorithm to provide a PRNG that has both +the theoretical Devaney's chaos property and the practical +property of succeeding NIST statistical battery of tests. +To achieve this, it has been proven in +this article that it is sufficient +for the iteration graph to be strongly connected, +and it is necessary and sufficient for its Markov probability matrix to be doubly stochastic. +However, they do not purpose conditions +to provide such Boolean maps. +Admittedly, sufficient conditions +to retrieve Boolean maps whose graphs are +strongly connected are given, but it remains to further filter those whose +Markov matrix is doubly stochastic. +This approach suffers from delaying the second requirement to a final step +whereas this is a necessary condition. +In this position article, we provide a completely new approach +to generate Boolean functions, whose Markov matrix is doubly stochastic and whose +graph of iterations is strongly connected. +Furthermore the rate of convergence is always taken into consideration to provide +PRNG with good statistical properties. + + +This research work is organized as follows. +It firstly recall some preliminaries that make the document self-contained (Section~\ref{sec:preliminaries}), +The next section (Section~\ref{sec:DSSC}) shows how this problem can be theoretically solved with a classical constraint logic programming. +Section~\ref{sec:hamiltonian} is the strongest contribution of this work. +It presents the main algorithm to generate Boolean maps with all the required properties and +proves that such a construction is correct. +Statistical evaluations are then presented in Section~\ref{sec:exp}. +Conclusive remarks, open problems, and perspectives are +finally provided. + + +\vspace{-2em} +\section{\uppercase{Preliminaries}}\label{sec:preliminaries} +\vspace{-1em} +In what follows, we consider the Boolean algebra on the set +$\Bool=\{0,1\}$ with the classical operators of conjunction '.', +of disjunction '+', of negation '$\overline{~}$', and of +disjunctive union $\oplus$. + +Let $n$ be a positive integer. A {\emph{Boolean map} $f$ is +a function from the Boolean domain + to itself +such that +$x=(x_1,\dots,x_n)$ maps to $f(x)=(f_1(x),\dots,f_n(x))$. +Functions are iterated as follows. +At the $t^{th}$ iteration, only the $s_{t}-$th component is +``iterated'', where $s = \left(s_t\right)_{t \in \mathds{N}}$ is a sequence of indices taken in $\llbracket 1;n \rrbracket$ called ``strategy''. Formally, +let $F_f: \llbracket1;n\rrbracket\times \Bool^{n}$ to $\Bool^n$ be defined by +\[ +F_f(i,x)=(x_1,\dots,x_{i-1},f_i(x),x_{i+1},\dots,x_n). +\] +Then, let $x^0\in\Bool^n$ be an initial configuration +and $s\in +\llbracket1;n\rrbracket^\Nats$ be a strategy, +the dynamics are described by the recurrence +\begin{equation}\label{eq:asyn} +x^{t+1}=F_f(s_t,x^t). +\end{equation} + + +Let be given a Boolean map $f$. Its associated +{\emph{iteration graph}} $\Gamma(f)$ is the +directed graph such that the set of vertices is +$\Bool^n$, and for all $x\in\Bool^n$ and $i\in \llbracket1;n\rrbracket$, +the graph $\Gamma(f)$ contains an arc from $x$ to $F_f(i,x)$. + +\begin{xpl} +Let us consider for instance $n=3$. Let +$f^*: \Bool^3 \rightarrow \Bool^3$ be defined by +$f^*(x_1,x_2,x_3)=(x_2 \oplus x_3, x_1 \oplus \overline{x_3},\overline{x_3})$. +The iteration graph $\Gamma(f^*)$ of this function is given in +Figure~\ref{fig:iteration:f*}. + +\vspace{-1em} +\begin{figure}[ht] +\begin{center} +\includegraphics[scale=0.5]{iter_f0b.eps} +\end{center} +\vspace{-0.5em} +\caption{Iteration Graph $\Gamma(f^*)$ of the function $f^*$}\label{fig:iteration:f*} +\end{figure} +\end{xpl} + +\vspace{-0.5em} +It is easy to associate a Markov Matrix $M$ to such a graph $G(f)$ +as follows: + +$M_{ij} = \frac{1}{n}$ if there is an edge from $i$ to $j$ in $\Gamma(f)$ and $i \neq j$; $M_{ii} = 1 - \sum\limits_{j=1, j\neq i}^n M_{ij}$; and $M_{ij} = 0$ otherwise. + +\begin{xpl} +The Markov matrix associated to the function $f^*$ is +$$ +\dfrac{1}{3} +\left( +\begin{array}{llllllll} +1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ +1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 \\ +0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 \\ +0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\ +1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ +0 & 0 & 0 & 0 & 1 & 1 & 0 & 1 \\ +0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 \\ +0 & 0 & 0 & 1 & 0 & 0 & 1 & 1 +\end{array} +\right) +$$ + + +\end{xpl} + + +It is usual to check whether rows of such kind of matrices +converge to a specific +distribution. +Let us first recall the \emph{Total Variation} distance $\tv{\pi-\mu}$, +which is defined for two distributions $\pi$ and $\mu$ on the same set +$\Omega$ by: +$$\tv{\pi-\mu}=\max_{A\subset \Omega} |\pi(A)-\mu(A)|.$$ +% It is known that +% $$\tv{\pi-\mu}=\frac{1}{2}\sum_{x\in\Omega}|\pi(x)-\mu(x)|.$$ + +Let then $M(x,\cdot)$ be the +distribution induced by the $x$-th row of $M$. If the Markov chain +induced by +$M$ has a stationary distribution $\pi$, then we define +$$d(t)=\max_{x\in\Omega}\tv{M^t(x,\cdot)-\pi}.$$ +Intuitively $d(t)$ is the largest deviation between +the distribution $\pi$ and $M^t(x,\cdot)$, which +is the result of iterating $t$ times the function. +Finally, let $\varepsilon$ be a positive number, the \emph{mixing time} +with respect to $\varepsilon$ is given by +$$t_{\rm mix}(\varepsilon)=\min\{t \mid d(t)\leq \varepsilon\}.$$ +It defines the smallest iteration number +that is sufficient to obtain a deviation lesser than $\varepsilon$. +% Notice that the upper and lower bounds of mixing times cannot +% directly be computed with eigenvalues formulae as expressed +% in~\cite[Chap. 12]{LevinPeresWilmer2006}. The authors of this latter work +% only consider reversible Markov matrices whereas we do no restrict our +% matrices to such a form. + + + +Let us finally present the pseudorandom number generator $\chi_{\textit{14Secrypt}}$ +which is based on random walks in $\Gamma(f)$. +More precisely, let be given a Boolean map $f:\Bool^n \rightarrow \Bool^n$, +a PRNG \textit{Random}, +an integer $b$ that corresponds to an awaited mixing time, and +an initial configuration $x^0$. +Starting from $x^0$, the algorithm repeats $b$ times +a random choice of which edge to follow and traverses this edge. +The final configuration is thus outputted. +This PRNG is formalized in Algorithm~\ref{CI Algorithm}. + + + +\vspace{-1em} +\begin{algorithm}[ht] +%\begin{scriptsize} +\KwIn{a function $f$, an iteration number $b$, an initial configuration $x^0$ ($n$ bits)} +\KwOut{a configuration $x$ ($n$ bits)} +$x\leftarrow x^0$\; +\For{$i=0,\dots,b-1$} +{ +$s\leftarrow{\textit{Random}(n)}$\; +$x\leftarrow{F_f(s,x)}$\; +} +return $x$\; +%\end{scriptsize} +\caption{Pseudo Code of the $\chi_{\textit{14Secrypt}}$ PRNG} +\label{CI Algorithm} +\end{algorithm} +\vspace{-0.5em} +This PRNG is a particularized version of Algorithm given in~\cite{BCGR11}. +Compared to this latter, the length of the random +walk of our algorithm is always constant (and is equal to $b$) whereas it +was given by a second PRNG in this latter. +However, all the theoretical results that are given in~\cite{BCGR11} remain +true since the proofs do not rely on this fact. + +Let $f: \Bool^{n} \rightarrow \Bool^{n}$. +It has been shown~\cite[Th. 4, p. 135]{BCGR11}} that +if its iteration graph is strongly connected, then +the output of $\chi_{\textit{14Secrypt}}$ follows +a law that tends to the uniform distribution +if and only if its Markov matrix is a doubly stochastic matrix. + +Let us now present a method to +generate functions +with Doubly Stochastic matrix and Strongly Connected iteration graph, + denoted as DSSC matrix. + + + +\vspace{-2em} +\section{\uppercase{Generation of DSSC Matrices}}\label{sec:DSSC} +\vspace{-1em} +This aim of this section is to show +that finding DSSC matrices from a hypercube +is a typical finite domain satisfaction +problem, classically denoted as +Constraint Logic Programming on Finite Domains (CLPFD). +This part is addressed in the first section. Next, we analyse the first +results to provide a generation of DSSC matrices with small mixing times. + +\vspace{-1em} +\subsection{Constraint Logic Programming on Finite Domains} +\vspace{-1em} +First of all, +let $n$ be the number of elements. In order to avoid fractions +in this article, we consider here that the +sum of each column and each row is $n$. It can easily be normalized to 1. +The goal is thus to find all the $2^n\times 2^n$ matrices $M$ +such that: + +\begin{enumerate} +\item $M_{ij}$ is 0 if $j$ is not a neighbor of $i$, \textit{i.e.}, + there is no edge from $i$ to $j$ in the $n$-cube. +\item $0 \le M_{ii} \le n$: the number of loops around $i$ is lesser than $n$ +\item Otherwise $0 \le M_{ij} \le 1$: if the edge from $i$ to $j$ is kept, +$M_{ij}$ is 1, and 0 otherwise. +\item For any index of line $i$, $1 \le i\le 2^n$, $n = \sum_{1 \le j\le 2^n} M_{ij}$: + the matrix is right stochastic. +\item For any index of column $j$, + $1 \le j\le 2^n$, $n = \sum_{1 \le i\le 2^n} M_{ij}$: + the matrix is left stochastic. +\item All the values of $\sum_{1\le k\le 2^n}M^k$ are strictly positive, \textit{i.e.}, the induced graph is strongly connected. +\end{enumerate} + + +Since these variables range into finite integer domains with sum and +product operations, this problem can be theoretically handled by +Constraint Logic Programming on Finite Domains (CLPFD), as implemented +in prolog. + +Finally, we define the relation $\mathcal{R}$, which is established on the +two functions +$f$ and $g$ if the iteration graphs $\Gamma(f)$ and $\Gamma(g)$ +are isomorphic. +Obviously, this is an equivalence relation. + + +\vspace{-1em} +\subsection{Analysis of the Approach} +\vspace{-1em} + +When executed on a personal computer, the prolog algorithm finds +in less than 1 second the 49 solutions when $n$ is 2, where only 2 are not equivalent, and in less than 1 minute the 27642 solutions where only 111 are +not equivalent when $n$ is 3. But it does not achieve the generation of +all the solutions when $n$ is 4. +This approach suffers from not being efficient enough for large $n$ due to +a \emph{generate and test} approach, despite the efficiency of the native +backtrack of in CLP. + +However, first results for small values of $n$ have been evaluated. +More precisely, non equivalent generated +functions have been compared according to their +ability to efficiently produce uniformly distributed outputs, \textit{i.e.}, +to have the smallest mixing time. + +\begin{xpl} +Table~\ref{table:mixing:3} gives the 5 best Boolean functions +ordered by their mixing times (MT) in the third column for $\varepsilon=10^{-5}$. +\begin{table}[ht] +\begin{small} +$$ +\begin{array}{|l|l|l|} +\hline +\textrm{Name} & \textrm{Image} & \textrm{MT}\\ +\hline +f^* & (x_2 \oplus x_3, x_1 \oplus \overline{x_3},\overline{x_3}) & 16 \\ +\hline +f^a & (x_2 \oplus x_3, \overline{x_1}\overline{x_3} + x_1\overline{x_2}, +\overline{x_1}\overline{x_3} + x_1x_2) & 17 \\ +\hline +f^b & (\overline{x_1}(x_2+x_3) + x_2x_3,\overline{x_1}(\overline{x_2}+\overline{x_3}) + \overline{x_2}\overline{x_3}, & \\ +& \qquad \overline{x_3}(\overline{x_1}+x_2) + \overline{x_1}x_2) & 26 \\ +\hline +f^c & (\overline{x_1}(x_2+x_3) + x_2x_3,\overline{x_1}(\overline{x_2}+\overline{x_3}) + \overline{x_2}\overline{x_3}, & \\ +& \overline{x_3}(\overline{x_1}+x_2) + \overline{x_1}x_2) & 29 \\ +\hline +f^d & (x_1\oplus x_2,x_3(\overline{x_1}+\overline{x_2}),\overline{x_3}) & 30 \\ +\hline +% [3, 4, 7, 0, 1, 6, 5, 2], #16 +% [3, 4, 7, 0, 2, 6, 5, 1], #17 +% [3, 6, 7, 5, 2, 0, 1, 4], #26 +% [3, 4, 7, 5, 2, 6, 1, 0], #29 +% [3, 2, 5, 6, 7, 0, 1, 4]] #30 +\end{array} +$$ +\end{small} +\caption{The 5 Boolean functions with smallest MT when $n=3$.}\label{table:mixing:3} +\end{table} +\end{xpl} + +A syntactical analysis of the functions for $n$=3 +does not help to understand +how to build a Boolean map with a small mixing time. +However the iteration graph of $f^*$ +(given in Figure~\ref{fig:iteration:f*}) +is the $3$-cube in which the cycle +$000,100,101,001,011,111,110,010,000$ +has been removed. +This cycle that visits each vertex exactly once is usually denotes as +\emph{Hamiltonian cycle}. +We are now focusing on the generation of DSSC matrices by +removing Hamiltonian cycles of the $n$-cube. + + +\vspace{-2em} +\section{\uppercase{Removing Hamiltonian Cycles}}\label{sec:hamiltonian} +\vspace{-1em} +The first theoretical section shows that this approach produces DSSC matrix, as wished. +The motivation to focus on balanced Gray code is then given in Sec.~\ref{sub:gray}. +We end this section by recalling an algorithm that aims at computing such codes (Section~\ref{sub:algo:gray}). + +\vspace{-1em} +\subsection{Theoretical Aspects of Removing Hamiltonian Cycles} +\vspace{-1em} + +We first have the following result on stochastic matrix and $n$-cube without +Hamiltonian cycle. + +\begin{theorem} +The Markov Matrix $M$ resulting from the $n$-cube in +which an Hamiltonian +cycle is removed, is doubly stochastic. +\end{theorem} +\begin{proof} +An Hamiltonian cycle visits each vertex exactly once. +For each vertex $v$ in the $n$-cube, +one ongoing edge $(o,v)$ and one outgoing edge $(v,e)$ +are thus removed. + +Let us consider the Markov matrix $M$ of the $n$-cube. +It is obviously doubly stochastic. +Since we exactly remove one outgoing edge, the value of $M_{ve}$ decreases +from $\frac{1}{n}$ to 0 and +$M_{vv}$ is $\frac{1}{n}$. The $M$ matrix is stochastic again. +Similarly for ongoing edge, since one ongoing edge is dropped for each +vertex, the value of $M_{ov}$ decreases +from $\frac{1}{n}$ to $0$. Moreover, since $M_{vv}$ is $\frac{1}{n}$, +the sum of values in column $v$ is $1$, and $M$ is doubly stochastic. +\end{proof} + +The following result states that the $n$-cube without one +Hamiltonian cycle +has the awaited property with regard to the connectivity. + +\begin{theorem} +The iteration graph issued from the $n$-cube where an Hamiltonian +cycle is removed is strongly connected. +\end{theorem} +\begin{proof} +We consider the reverse cycle $r$ of the Hamiltonian cycle $c$. +There is no edge that belongs to both $r$ and $c$: otherwise $c$ +would contain one vertex twice. Thus, no edges of $r$ has been removed. +The cycle $r$ is obviously an Hamiltonian cycle and contains all the nodes. +Any node of the $n$-cube where $c$ has been removed can thus reach any node. +The iteration graph is thus strongly connected. +\end{proof} + +Removing an Hamiltonian cycle in the $n$-cube solves thus the DSSC constraint. +We are then left to focus on the generation of Hamiltonian cycles in the +$n$-cube. Such a problem is equivalent to find Gray codes, \textit{i.e.}, +to find a sequence of $2^n$ codewords ($n$-bits strings) +where two successive elements differ in only one bit position. +The next section is dedicated to these codes. + +\vspace{-1em} +\subsection{Linking to (Totally) Balanced Gray Codes}\label{sub:gray} +\vspace{-1em} +Many research works~\cite{journals/combinatorics/BhatS96,VanSup04,journals/combinatorics/FlahiveB07} +have addressed the subject of finding Gray codes. +Since our approach is based on removing a cycle, we are concerned +with cyclic Gray codes, \textit{i.e.}, sequences where the last codeword +differs in only one bit position from the first one. + +Let $n$ be a given integer. As far as we know, +the exact number of Gray codes in $\Bool^n$ is not known but +a lower bound, $$\left(\frac{n*\log2}{e \log \log n}*(1 - o(1))\right)^{2^n}$$ +has been given in~\cite{Feder:2009:NTB:1496397.1496515}. +For example, when $n$ is $6$, such a number is larger than $10^{13}$. + +To avoid this combinatorial explosion, we want to +restrict the generation to any Gray code +such that the induced graph of iteration $\Gamma(f)$ is +``uniform''. In other words, if we count in $\Gamma(f)$ +the number of edges that modify the bit $i$, for $1 \le i \le n$, +all these values have to be close to each other. +Such an approach is equivalent to restrict the search of cyclic Gray codes +which are uniform too. + +This notion can be formalized as follows. Let $L = w_1, w_2, \dots, w_{2^n}$ be the sequence +of a $n$-bits cyclic Gray code. Let $S = s_1, s_2, \dots, s_{2^n}$ be the +transition sequence where $s_i$, $1 \le i \le 2^n$ indicates which bit position changes between +codewords at index $i$ and $i+1$ modulo $2^n$. +Let $\textit{TC}_n : \{1,\dots, n\} \rightarrow \{0, \ldots, 2^n\}$ the \emph{transition count} function +that counts the number of times $i$ occurs in $S$, \textit{i.e.}, the number of times +the bit $i$ has been switched in $L$. +The Gray code is \emph{totally balanced} if $\textit{TC}_n$ is constant (and equal to $\frac{2^n}{n}$). +It is \emph{balanced} if for any two bit indices $i$ and $j$, +$|\textit{TC}_n(i) - \textit{TC}_n(j)| \le 2$. + +\begin{xpl} +Let $L^*$ be the Gray code $000,100,101,001,011,111,110,010$ +that corresponds to the Hamiltonian cycle that has been removed in $\Gamma(f^*)$. +It is balanced since its transition sequence is $S=3,1,3,2,3,1,3,2$ +and its transition count function is +$\textit{TC}_3(1)= \textit{TC}_3(2)=2$ and $\textit{TC}_3(3)=4$. + +Let $L^4$ be the cyclic Gray code +$0000, 0010, 0110, 1110, 1111, 0111, 0011, 0001, 0101,$ +$0100, 1100, 1101, 1001, 1011, 1010, 1000$. + Since $S=2,3,4,1,4,3,2,3,1,4,1,3,2,1,2,4$ $\textit{TC}_4$ is equal to 4 everywhere, this code +is thus totally balanced. +\end{xpl} + +\vspace{-1em} +\subsection{Induction-Based Generation of Balanced Gray Codes}\label{sub:algo:gray} +\vspace{-1em} + +The algorithm we adapt is based on the ``Construction B''~\cite{VanSup04} we recall now. +This method inductively constructs $n$-bits Gray code given a $n-2$-bit Gray code. + +It starts with the transition sequence $S_{n-2}$ of such code. + +\begin{enumerate} +\item \label{item:nondet}Let $l$ be an even positive integer. Find +$u_1, u_2, \dots , u_{l-2}, v$ (maybe empty) subsequences of $S_{n-2}$ +such that $S_{n-2}$ is the concatenation of +$$ +s_{i_1}, u_0, s_{i_2}, u_1, s_{i_3}, u_2, . . . , s_{i_l-1}, u_{l-2}, s_{i_l}, v +$$ +where $i_1 = 1$, $i_2 = 2$, and $u_0 = \emptyset$ (the empty sequence). +\item Replace in $S_{n-2}$ the sequences $u_0, u_1, u_2, \ldots, u_{l-2}$ + by + $n - 1, u'(u_1,n - 1, n) , u'(u_2,n, n - 1), u'(u_3,n - 1,n), \dots, u'(u_{l-2},n, n - 1)$ + respectively, where $u'(u,x,y)$ is the sequence $u,x,u^R,y,u$ such that + $u^R$ is $u$ in reversed order. The obtained sequence is further denoted as $U$. +\item Construct the sequences $V=v^R,n,v$, $W=n-1,S_{n-2},n$, and let $W'$ be $W$ where the first +two elements have been exchanged. +\item The transition sequence $S_{n}$ is thus the concatenation $U^R, V, W'$. +\end{enumerate} + +It has been proven in~\cite{VanSup04} that +$S_{n}$ is transition sequence of a cyclic $n$-bits Gray code +if $S_{n-2}$ is. +However, the step~\ref{item:nondet} is not a constructive +step that precises how to select the subsequences which ensures that +yielded Gray code is balanced. + +Let us now evaluate the number of subsequences $u$ +than can be produced. Since $s_{i_1}$ and $s_{i_2}$ are well +defined, we have to chose the $l-2$ elements of $s_3,s_4,\dots,s_{2^{n-2}}$ +that become $s_{i_3},\dots, s_{i_l}$. Let $l = 2l'$. +There are thus +$$ +\#_n = \sum_{l'=1}^{2^{n-3}} {2^{n-2}-2 \choose 2l'-2} +$$ +distinct subsequences $u$. +Numerical values of $\#_n$ are given in table~\ref{table:combinations}. +Even for small values of $n$, it is not reasonable to hope to evaluate the whole +set of subsequences. +\begin{table}[ht] +\begin{scriptsize} +\begin{center} +\begin{tabular}{|l|l|l|l|l|l|l|l|l|} +\hline +$n$ & 5 & 6 & 7 & 8 & 9 \\ +\hline +$\#_n$ & +31 & 8191 & 5.3e8 & 2.3e18 & 4.2e37\\ +\hline +$\#'_n$ & +15 & 3003 & 1.4e8 & 4.5e17 & 1.6e36 \\ +\hline +\end{tabular} +\end{center} +\end{scriptsize} +\caption{Number of distinct $u$ subsequences.}\label{table:combinations} +\end{table} + +However, it is shown in the article that $\textit{TC}_n(n-1)$ and $\textit{TC}_n(n)$ are +equal to $l$. Since this step aims at generating (totally) balanced Gray codes, +we have set $l$ to be the largest even integer less or equal than $\frac{2^n}{n}$. +This improvement allows to reduce the number of subsequences to study. +Examples of such cardinalities are given in table~\ref{table:combinations} and are refered as +$\#'_n$. + +Finally, the table~\ref{table:nbFunc} gives the number of non-equivalent functions issued from +(totally) balanced Gray codes that can be generated +with the approach presented in this article with respect to the number of bits. In other words, it corresponds to the size of the class of generators that can be produced. + +\begin{table}[ht] +\begin{center} +\begin{scriptsize} +\begin{tabular}{|l|c|c|c|c|} +\hline +$n$ & 3 & 4 & 5 & 6 \\ +\hline +nb. of functions & 1 & 1 & 2 & 1332 \\ +\hline +\end{tabular} +\end{scriptsize} +\end{center} +\caption{Generators Numbers w.r.t. bits Numbers.} +\label{table:nbFunc} +\end{table} + + +\vspace{-2em} +\section{\uppercase{Experiments}}\label{sec:exp} +\vspace{-1em} +We have directly implemented the algorithm given in Figure~\ref{CI Algorithm}. +For function $f$ and our experiments $b$ is set +with the value given in the fourth column of Table~\ref{table:nc}. + +% We present in Algorithm~\ref{CI} the method +% that allows to take any chaotic function as the core of a pseudo +% random number generator. Among the parameters, it takes the +% number b of minimal iterations that have to be executed to +% get a uniform like distribution. 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of 494999 + 319621 string characters out of 6180228 + 426069 words of memory out of 5000000 + 19369 multiletter control sequences out of 15000+600000 + 11749 words of font info for 38 fonts, out of 8000000 for 9000 + 14 hyphenation exceptions out of 8191 + 48i,10n,56p,541b,192s stack positions out of 5000i,500n,10000p,200000b,80000s + +Output written on markov.pdf (4 pages, 146960 bytes). +PDF statistics: + 233 PDF objects out of 1000 (max. 8388607) + 69 compressed objects within 1 object stream + 0 named destinations out of 1000 (max. 500000) + 13 words of extra memory for PDF output out of 10000 (max. 10000000) + diff --git a/crCOUCHOT14/markov.pdf b/crCOUCHOT14/markov.pdf new file mode 100644 index 0000000..e766a50 Binary files /dev/null and b/crCOUCHOT14/markov.pdf differ diff --git a/crCOUCHOT14/markov.tex b/crCOUCHOT14/markov.tex new file mode 100644 index 0000000..004dc60 --- /dev/null +++ b/crCOUCHOT14/markov.tex @@ -0,0 +1,264 @@ +\documentclass{article} +%\usepackage{prentcsmacro} +%\sloppy + +\usepackage[latin1]{inputenc} +\usepackage[T1]{fontenc} +\usepackage[english]{babel} +\usepackage{amsmath,amssymb,latexsym,eufrak,euscript} +\usepackage{subfigure,pstricks,pst-node,pst-coil} + + +\usepackage{url,tikz} +\usepackage{pgflibrarysnakes} + +\usepackage{multicol} + +\usetikzlibrary{arrows} +\usetikzlibrary{automata} +\usetikzlibrary{snakes} +\usetikzlibrary{shapes} + +%% \setlength{\oddsidemargin}{15mm} +%% \setlength{\evensidemargin}{15mm} \setlength{\textwidth}{140mm} +%% \setlength{\textheight}{219mm} \setlength{\topmargin}{5mm} +\newtheorem{theorem}{Theorem} +%\newtheorem{definition}[theorem]{Definition} +% %\newtheorem{defis}[thm]{D\'efinitions} + \newtheorem{example}[theorem]{Example} +% %\newtheorem{Exes}[thm]{Exemples} +\newtheorem{lemma}[theorem]{Lemma} +\newtheorem{proposition}[theorem]{Proposition} +\newtheorem{construction}[theorem]{Construction} +\newtheorem{corollary}[theorem]{Corollary} +% \newtheorem{algor}[thm]{Algorithm} +%\newtheorem{propdef}[thm]{Proposition-D\'efinition} +\newcommand{\mlabel}[1]{\label{#1}\marginpar{\fbox{#1}}} +\newcommand{\flsup}[1]{\stackrel{#1}{\longrightarrow}} + +\newcommand{\stirlingtwo}[2]{\genfrac{\lbrace}{\rbrace}{0pt}{}{#1}{#2}} +\newcommand{\stirlingone}[2]{\genfrac{\lbrack}{\rbrack}{0pt}{}{#1}{#2}} + +\newenvironment{algo} +{ \vspace{1em} +\begin{algor}\mbox +\newline \vspace{-0.1em} +\begin{quote}\begin{rm}} +{\end{rm}\end{quote}\end{algor}\vspace{-1.5em}\vspace{2em}} +%\null \hfill $\diamondsuit$ \par\medskip \vspace{1em}} + +\newenvironment{exe} +{\begin{example}\rm } +{\end{example} +%\vspace*{-1.5em} +%\null \hfill $\triangledown$ \par\medskip} +%\null \hfill $\triangledown$ \par\medskip \vspace{1em}} +} + + +\newenvironment{proof} +{ \noindent {\sc Proof.\/} } +{\null \hfill $\Box$ \par\medskip \vspace{1em}} + + +\newcommand {\pb}[3] { +\medskip +\noindent +\fbox{ +\parbox[c]{11.5cm}{ +{\bf #1} + +\noindent +{\bf Input:} #2 + +\noindent +{\bf Output:} #3 + +\medskip +} +} + +\medskip +} + + +\newcommand {\tv}[1] {\lVert #1 \rVert_{\rm TV}} +\def \top {1.8} +\def \topt {2.3} +\def \sp {\hspace*{0.8cm}} +\def \A {\mathcal{A}} +\def \P {\mathcal{P}} +\def \B {\mathcal{B}} +\def \C {\mathcal{C}} +\def \D {\mathcal{D}} +\def \R {\mathcal{R}} +\def \T {\mathfrak{T}} +\def \M {\mathcal{M}} +\def \ov {\overline} + +\begin{document} +\label{firstpage} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Mathematical Backgroung} + +Let $G$ be a finite group. For any subset $S$ of $G$ we denote by +$$ the subgroup of $G$ generated by $S$. +If $=G$, $S$ is a generator of $G$. + + + +Let $\pi$, $\mu$ be two distribution on a same set $\Omega$. The total +variation distance between $\pi$ and $\mu$ is denoted $\tv{\pi-\mu}$ and is +defined by +$$\tv{\pi-\mu}=\max_{A\subset \Omega} |\pi(A)-\mu(A)|.$$ It is known that +$$\tv{\pi-\mu}=\frac{1}{2}\sum_{x\in\Omega}|\pi(x)-\mu(x)|.$$ Moreover, if +$\nu$ is a distribution on $\Omega$, one has +$$\tv{\pi-\mu}\leq \tv{\pi-\nu}+\tv{\nu-\mu}$$ + +Let $P$ be the matrix of a markov chain on $\Omega$. $P(x,\cdot)$ is the +distribution induced by the $x$-th row of $P$. If the markov chain induced by +$P$ has a stationary distribution $\pi$, then we define +$$d(t)=\max_{x\in\Omega}\tv{P^t(x,\cdot)-\pi},$$ +and + +$$t_{\rm mix}(\varepsilon)=\min\{t \mid d(t)\leq \varepsilon\}.$$ +One can prove that + +$$t_{\rm mix}(\varepsilon)\leq \lceil\log_2(\varepsilon^{-1})\rceil t_{\rm mix}(\frac{1}{4})$$ + +It is known that $d(t+1)\leq d(t)$. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{PRNG and random walk on Cayley graphs} + + +Let $S$ be a generator of $\mathbb{B}^N$ such that if $s\in S$, then +$-s\in S$. Let $\nu$ be a distribution on $S$ such that +$\nu(s)=\nu(-s)$. The matrix $P^\nu$, or just $P^\nu$, or just $P$, +is the matrix defined by: $P^\nu(x,y)=\nu(y-x)$ if $x-y\in S$ and $0$ +otherwise. $P_S^\nu$ is the $\nu$-random walk on the $S$-Cayley graph +of $G$. + +A general results on random walks claims that the uniform distribution +is stationnary for $P$. Moreover, if $\nu(s)>0$ for each $s$, then +this is the limit distribution. + +Let $\mathcal{P}$ be finite subset of $\mathbb{N}$ and $\mu$ a distribution +on $\mathcal{P}$. Set +$$ P_{\mathcal{P},\mu}=\sum_{k\in\mathcal{P}}\mu(k)P^k.$$ + + +With the above notation, $P_{\mathcal{P},\mu}$ is the matrix of the markov +chain corresponding to the PRNG defined by Christophe, where $S$ corresponds +to the boolean functions and $\mu$ si the probability of choosing elements +of $\mathcal{P}$. + + +\begin{exe} +For instance let $e_i$ be the vector of $\mathbb{B}^N$ whose $i$-th +componenent is $1$ and all other compoennts are null. Let $e_0=0$ and +$S=\{e_i\mid 0\leq i\leq N\}$. Choosing $\nu(e_i)=\dfrac{1}{N+1}$, we +obtain the random walk defined by the {\em bit negation} of the paper +by Christophe and JEF. +The associated matrix will be denoted $P_1$. + Choosing $\mathcal{P}=\{10,11\}$ and +$\mu(10)=\mu(11)=\dfrac{1}{2}$ provides the PRNG with steps of lengths +10 or 11 with the same probability. +\end{exe} + + +\begin{exe} +With the same notation, choosing the same $S$, but +$\nu(e_i)=\dfrac{1}{2n}$ if $i \geq 1$ and $\nu(e_0)=1/2$ leads to the +the classical lazy random walk on $\mathbb{B}^N$ (also known as the +lazy random walk on the hypercube or as the Ehrenfest Urn Model). +The associated matrix will be denoted $P_2$. +\end{exe} + +\begin{exe} +Choosing $S=G$ and the uniform distribution for $\nu$ corresponds to +the xor approach of the paper with Raphael. +\end{exe} + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Results} + +The main result is that if the minimal element of $\mathcal{P}$ is +greater or equal to the mixing time of $P$, then the PRNG provides a distribution +whose distance to the uniform distribution is at most $\varepsilon$. + +Let $t_P(\varepsilon)$ be the $\varepsilon$ mixing time for $P$. +Without loss of generality we assume that if $k\in \mathcal{P}$, then +$\mu(k)>0$. + +\begin{proposition} +Let $k_0=\min \{ k\mid k\in \mathcal{P}\}$. +If $k_0 \geq +t_P(\varepsilon)$, and if $\nu(s)>0$ for all $s\in S$, then one has +$\tv{P_{\mathcal{P},\mu}(x,\cdot)-\pi}\leq \varepsilon$, where $\pi$ +is the uniform distribution. +\end{proposition} + +\begin{proof} +The fact that $\nu(s)>0$ for all $s\in S$ ensures that the uniform +distribution is the limits of the markov chains induced by $P$ +(classical results on random walks). + +Now, +\begin{align*} +\tv{P_{\mathcal{P},\mu}(x,\cdot)-\pi}&=\tv{\sum_{k\in\mathcal{P}}\mu(k)P^k(x,\cdot)-\pi}\\ +&=\frac{1}{2}\sum_{y\in\mathbb{B}^N}|\sum_{k\in\mathcal{P}}\mu(k)P^k(x,y)-\dfrac{1}{2^N}|\\ +&=\frac{1}{2}\sum_{y\in\mathbb{B}^N}|\sum_{k\in\mathcal{P}}\mu(k)P^k(x,y)-\dfrac{1}{2^N}\sum_{k\in\mathcal{P}}\mu(k)|\\ +&=\frac{1}{2}\sum_{y\in\mathbb{B}^N}|\sum_{k\in\mathcal{P}}\mu(k)(P^k(x,y)-\dfrac{1}{2^N})|\\ +&\leq \frac{1}{2}\sum_{y\in\mathbb{B}^N}\sum_{k\in\mathcal{P}}\mu(k)|P^k(x,y)-\dfrac{1}{2^N}|\\ +&\leq \sum_{k\in\mathcal{P}}\mu(k)\left(\frac{1}{2}\sum_{y\in\mathbb{B}^N}|P^k(x,y)-\dfrac{1}{2^N}|\right)\\ +&\leq \sum_{k\in\mathcal{P}}\mu(k)\tv{P^k(x,\cdot)-\pi}\\ +&\leq \sum_{k\in\mathcal{P}}\mu(k)\varepsilon\\ +&\leq \varepsilon\\ +\end{align*} +\end{proof} + + +Therfore it suffices to study the mixing time of $P$. + + + +%%%%%%%%%%%%%%%%%%%% +\section{Mixing time of $P_1$} + +See the Ehrenfest Urn Model. One can prove that for $P_1$, + +$$t_{\rm mix}(\varepsilon)\leq N \log N+ \log (\frac{1}{\varepsilon})N.$$ + +Better results exist see \cite[page 83, page 267]{mixing} + +%%%%%%%%%%%%%%%%%%%% +\section{Mixing time of $P_2$} + +In practice one can compute egenvalues and use \cite[page 155]{mixing}. + +There are theoretical results \cite[page 321-322]{rwfg} and~\cite{WilsonHyper}. + + +%%%%%%%%%%%%%%%%%%%% +\section{To do} + +Experiments for computing mixing time for $P_2$. + +Experiments for other $P$ (handly built) + +Which $\varepsilon$ makes possible to pass statistical tests for our PRNGs. Other tests can be performed. + +%%%%%%%%%%%%%%%%%%%%%% +\section{Future} + +Look at \cite{rwfg} for theoretical results. Explore random random walk on the hypercube. + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\bibliographystyle{alpha} +\bibliography{markovbib} +\end{document} diff --git a/crCOUCHOT14/texput.log b/crCOUCHOT14/texput.log new file mode 100644 index 0000000..cbe53d2 --- /dev/null +++ b/crCOUCHOT14/texput.log @@ -0,0 +1,21 @@ +This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013/Debian) (format=pdflatex 2014.4.22) 12 JUL 2014 11:23 +entering extended mode + restricted \write18 enabled. + %&-line parsing enabled. +**14Mons.tex + +! Emergency stop. +<*> 14Mons.tex + +End of file on the terminal! + + +Here is how much of TeX's memory you used: + 3 strings out of 494999 + 107 string characters out of 6180228 + 46040 words of memory out of 5000000 + 3324 multiletter control sequences out of 15000+600000 + 3640 words of font info for 14 fonts, out of 8000000 for 9000 + 14 hyphenation exceptions out of 8191 + 0i,0n,0p,1b,6s stack positions out of 5000i,500n,10000p,200000b,80000s +! ==> Fatal error occurred, no output PDF file produced! diff --git a/example.bib b/example.bib new file mode 100644 index 0000000..49a8286 --- /dev/null +++ b/example.bib @@ -0,0 +1,19 @@ + +@INPROCEEDINGS{Moore99, + AUTHOR = "R. Moore and J. Lopes", + TITLE = "Paper templates", + BOOKTITLE = "TEMPLATE'06, 1st International Conference on Template Production", + YEAR = "1999", + publisher = "SCITEPRESS", + file = F +} + +@BOOK{Smith98, + AUTHOR = "J. Smith", + TITLE = "The Book", + PUBLISHER = "The publishing company", + YEAR = "1998", + address = "London", + edition = "2nd", + file = F +} diff --git a/experiments/affiche3cube.py b/experiments/affiche3cube.py new file mode 100644 index 0000000..4fec3ba --- /dev/null +++ b/experiments/affiche3cube.py @@ -0,0 +1,36 @@ +from math import * + + +def bin(elem,n): + """Convertit un nombre en binaire""" + q = -1 + res =[0 for i in range(n)] + i = 1 + while q != 0: + q = elem // 2 + r = elem % 2 + res[n-i] = r + elem = q + i+=1 + return res + + +lc= [(0,0),(sqrt(3),-1),(2,0),(sqrt(3)+2,-1), + (0,2),(sqrt(3),1),(2,2),(sqrt(3)+2,1)] + + +cx,cy=10,10 +I=1 +lcp=[((cx+I*x),(cy-I*y)) for (x,y) in lc] + +n=3 +st ="" +for i in range(2**3): + x = bin(i,n) + xst = "" + for j in range(n): + xst += str(x[j]) + st += xst + " [label=\""+xst+"\", pos=\""+str(lcp[i][0])+","+str(lcp[i][1])+"!\"];\n" + +print st + diff --git a/experiments/analyseRes.py b/experiments/analyseRes.py new file mode 100644 index 0000000..337a17d --- /dev/null +++ b/experiments/analyseRes.py @@ -0,0 +1,66 @@ +import networkx as nx +from networkx.algorithms import isomorphism +from math import * +import numpy as np +from optparse import OptionParser + + + +f= "res3.txt" + + +def bin(elem,n): + """Convertit un nombre en binaire""" + q = -1 + res =[0 for i in range(n)] + i = 1 + while q != 0: + q = elem // 2 + r = elem % 2 + res[n-i] = r + elem = q + i+=1 + return res + +def dec(ch,n): + l = len(ch) + acc = 0 + for i in range(l): + if ch[i]==1: + acc = acc + 2**(n-i-1) + return acc + + + + +fd = open(f,'r') +laligne = fd.readline() + +laligne = laligne.replace('][','];[') +matrices = laligne.split(';') + + +for m in matrices[-1]: + try: + mp = eval(m) + #print mp + n= int(log(len(mp))/log(2)) + r=[] + for i in range(len(mp)): + o = bin(i,n) + imageb = bin(i,n) + for j in range(n): + op = bin(i,n) + op[j] = 1 -op[j] + if mp[i][dec(op,n)] != 0 : + imageb[j] = op[j] + image=dec(imageb,n) + r+=[image] + print r + except SyntaxError: + pass + + + + + diff --git a/experiments/calculeBorneInfNbGrayCodes.py b/experiments/calculeBorneInfNbGrayCodes.py new file mode 100644 index 0000000..3e2f9e7 --- /dev/null +++ b/experiments/calculeBorneInfNbGrayCodes.py @@ -0,0 +1,13 @@ +from math import * + + + +def log_2(x): + return log(x)/log(2) + +def bi(n): + o_1 = 0 + return pow((float(n*log_2(2))/(exp(1)*log_2(log_2(n)))*(1 - o_1)),2**n) + +for n in range(3,10): + print n, bi(n) diff --git a/experiments/calculeNbSouslistes.py b/experiments/calculeNbSouslistes.py new file mode 100644 index 0000000..5a933ee --- /dev/null +++ b/experiments/calculeNbSouslistes.py @@ -0,0 +1,30 @@ +from math import * + + +def binomialCoefficient(n, k): + if k < 0 or k > n: + return 0 + if k == 0 or k == n: + return 1 + diff = n - k + k = min(k, n - k) # take advantage of symmetry + c = 1 + for i in range(k): + c = c * (n - i) / (i + 1) + return c + +def bi(n): + return sum([binomialCoefficient(2**(n-2)-2, 2*lp-2) for lp in range(2**(n-1))[2:]]) + """ + k = 2**n/n + l = k if k%2 == 0 else k-1 + print "++", 2**(n-2)-2, l-2,binomialCoefficient(2**(n-2)-2, l-2) + return binomialCoefficient(2**(n-2)-2, l-2) + """ +stx ="" +sti ="" +for n in range(5,10): + stx+= str(n) + " & " + sti+= str(float(bi(n))) + " & " + +print stx, "\n", sti diff --git a/experiments/combinaisons.py b/experiments/combinaisons.py new file mode 100644 index 0000000..b0b840a --- /dev/null +++ b/experiments/combinaisons.py @@ -0,0 +1,62 @@ +from __future__ import generators +#!/usr/bin/env python + +__version__ = "1.0" + +"""xpermutations.py +Generators for calculating a) the permutations of a sequence and +b) the combinations and selections of a number of elements from a +sequence. Uses Python 2.2 generators. + +Similar solutions found also in comp.lang.python + +Keywords: generator, combination, permutation, selection + +See also: http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/105962 +See also: http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/66463 +See also: http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/66465 +""" + + +def xcombinations(items, n): + if n==0: yield [] + else: + for i in xrange(len(items)): + for cc in xcombinations(items[:i]+items[i+1:],n-1): + yield [items[i]]+cc + +def xuniqueCombinations(items, n): + if n==0: yield [] + else: + for i in xrange(len(items)): + for cc in xuniqueCombinations(items[i+1:],n-1): + yield [items[i]]+cc + +def xselections(items, n): + if n==0: yield [] + else: + for i in xrange(len(items)): + for ss in xselections(items, n-1): + yield [items[i]]+ss + +def xpermutations(items): + return xcombinations(items, len(items)) + +if __name__=="__main__": + print "Permutations of 'love'" + for p in xpermutations(['l','o','v','e']): print ''.join(p) + + print + print "Combinations of 2 letters from 'love'" + for c in xcombinations(['l','o','v','e'],2): print ''.join(c) + + print + print "Unique Combinations of 2 letters from 'love'" + for uc in xuniqueCombinations(['l','o','v','e'],2): print ''.join(uc) + + print + print "Selections of 2 letters from 'love'" + for s in xselections(['l','o','v','e'],2): print ''.join(s) + + print + print map(''.join, list(xpermutations('done'))) diff --git a/experiments/combinaisons.pyc b/experiments/combinaisons.pyc new file mode 100644 index 0000000..c1aa4a6 Binary files /dev/null and b/experiments/combinaisons.pyc differ diff --git a/experiments/evalPRNGs.txt b/experiments/evalPRNGs.txt new file mode 100644 index 0000000..388c817 --- /dev/null +++ b/experiments/evalPRNGs.txt @@ -0,0 +1,3 @@ +[[1032, 1057, 1008, 1068, 972, 960, 1012, 1008, 1001, 982, 1038, 992, 994, 1031, 1001, 977], [1052, 973, 995, 1031, 1038, 985, 995, 1018, 995, 1011, 1001, 982, 996, 963, 985, 1003], [1011, 995, 985, 1027, 1007, 987, 979, 991, 961, 976, 1033, 1050, 1000, 936, 1044, 987], [998, 1016, 1040, 1037, 985, 991, 984, 993, 1011, 998, 1001, 1044, 984, 998, 1032, 1076], [998, 998, 959, 1013, 1003, 1010, 990, 1005, 936, 1044, 973, 1017, 1018, 1046, 969, 1021], [969, 972, 1015, 978, 962, 902, 967, 1002, 976, 969, 1012, 1001, 961, 980, 992, 1069], [948, 994, 1029, 1088, 1036, 898, 1032, 984, 980, 949, 1021, 1004, 984, 987, 1009, 1028], [1034, 1042, 1004, 1034, 990, 964, 961, 991, 1000, 1030, 1007, 1024, 1034, 1005, 1010, 1034], [1006, 961, 1001, 936, 1002, 969, 1021, 973, 1041, 1025, 997, 1032, 1001, 1025, 949, 958], [1036, 1010, 961, 1013, 1048, 964, 995, 965, 999, 997, 983, 969, 987, 1045, 979, 1035], [1029, 964, 997, 999, 1056, 1051, 1005, 1039, 986, 995, 1003, 1012, 980, 1005, 937, 971], [981, 999, 1011, 1017, 999, 986, 1051, 1019, 1014, 984, 992, 1041, 1010, 1019, 1002, 959], [1025, 1005, 983, 996, 943, 1008, 915, 1091, 1004, 1066, 1040, 1014, 1004, 1015, 926, 937], [1018, 1029, 1019, 1010, 1009, 1054, 1027, 1016, 1010, 968, 987, 977, 1050, 1040, 954, 988], [982, 970, 1039, 980, 976, 1001, 1034, 1030, 958, 956, 967, 920, 986, 1014, 917, 947], [1013, 1038, 923, 961, 974, 997, 1003, 1039, 1025, 1037, 974, 1005, 983, 1047, 971, 1034]] +[[980, 1041, 1023, 990, 1052, 1021, 1018, 1003, 990, 970, 990, 973, 1034, 993, 1024, 1054, 1017, 974, 1059, 1039, 998, 917, 1012, 984, 1006, 981, 1007, 926, 942, 998, 1033, 1022, 1009, 1016, 996, 974, 996, 1018, 948, 1005, 1022, 1039, 985, 1005, 1009, 967, 921, 1012, 1024, 1001, 984, 943, 1004, 1011, 1010, 967, 1008, 995, 1008, 960, 972, 981, 970, 999], [994, 952, 984, 974, 998, 1005, 996, 999, 934, 998, 965, 1037, 1010, 972, 1031, 1038, 955, 992, 986, 1000, 1038, 1020, 989, 958, 1027, 990, 971, 987, 1014, 1015, 992, 1012, 983, 1019, 1015, 990, 987, 960, 984, 964, 1024, 1046, 1003, 1053, 1011, 1000, 996, 1010, 1046, 999, 938, 1016, 1016, 1008, 1035, 967, 1035, 1030, 1015, 1072, 1024, 1040, 979, 994], [1057, 1033, 998, 1035, 985, 1041, 986, 983, 1022, 980, 971, 995, 1023, 963, 982, 1011, 989, 939, 978, 998, 980, 983, 917, 1024, 1014, 965, 956, 1000, 999, 1018, 987, 992, 987, 971, 968, 975, 1022, 964, 1023, 1001, 985, 993, 1034, 1034, 1008, 1003, 1019, 1009, 937, 1061, 1000, 979, 983, 1017, 958, 963, 951, 1007, 997, 979, 977, 967, 1006, 1019], [957, 966, 998, 1010, 1062, 982, 975, 1011, 1005, 981, 924, 1019, 974, 1022, 1007, 976, 943, 983, 1008, 991, 996, 1015, 1082, 944, 974, 971, 980, 991, 1030, 1015, 990, 1025, 999, 1006, 980, 994, 1012, 1054, 955, 1007, 1039, 1004, 1022, 1015, 1002, 1005, 985, 1004, 1005, 967, 1008, 991, 973, 980, 986, 994, 1006, 1006, 942, 1037, 1012, 977, 1036, 975], [1037, 1024, 1030, 1012, 1011, 1026, 1020, 1017, 1009, 1033, 1013, 1011, 985, 1006, 1006, 1000, 997, 1060, 990, 991, 1065, 1033, 1008, 1044, 1052, 988, 949, 1024, 1006, 1031, 1009, 1030, 990, 973, 993, 984, 964, 1030, 989, 1028, 1006, 955, 1035, 997, 1012, 1020, 1028, 1002, 1023, 1016, 1020, 1000, 1061, 1014, 1022, 999, 986, 1030, 910, 1021, 983, 1020, 1004, 1040], [983, 1058, 1014, 1012, 981, 1017, 1063, 1016, 1007, 978, 978, 1013, 1006, 996, 987, 1000, 981, 1017, 1019, 1000, 1018, 998, 1027, 990, 1002, 1028, 989, 984, 994, 1021, 1018, 994, 972, 1019, 1031, 973, 1012, 1066, 1000, 1022, 1024, 1061, 927, 1004, 997, 1023, 1012, 1006, 986, 1050, 985, 1040, 999, 1015, 1032, 978, 1011, 994, 965, 985, 994, 1010, 1048, 962], [992, 990, 1011, 996, 991, 999, 1006, 989, 995, 1011, 1035, 988, 966, 1045, 1005, 977, 1018, 950, 1039, 1041, 1035, 995, 1030, 997, 989, 1005, 968, 1001, 1012, 1023, 1004, 937, 1021, 944, 1003, 1044, 989, 1022, 1029, 1035, 954, 988, 992, 1023, 936, 927, 961, 1085, 999, 999, 990, 1053, 985, 1036, 972, 980, 1041, 974, 1032, 956, 1028, 1029, 998, 1002], [973, 995, 985, 1012, 1023, 983, 1015, 992, 1040, 969, 968, 1010, 1009, 1055, 1009, 969, 1000, 1031, 1028, 981, 990, 925, 1034, 1024, 998, 996, 1005, 1039, 1040, 1012, 1029, 994, 940, 1062, 1001, 1011, 994, 994, 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+nbmaxiter = 6 +profM=n*pow(2,n) +prof = profM + +def bin(elem,n): + """Convertit un nombre en binaire""" + q = -1 + res =[0 for i in range(n)] + i = 1 + while q != 0: + q = elem // 2 + r = elem % 2 + res[n-i] = r + elem = q + i+=1 + return res + +def dec(ch,n): + l = len(ch) + acc = 0 + for i in range(l): + if ch[i]==1: + acc = acc + 2**(n-i-1) + return acc + + +def calculetmix(epsilon): + resTMIX=[] + global treatedlist + global n + if rf != False: + treatedlist =get_treatedlist(rf) + #print "taillle de la liste ",len(treatedlist) + n= int(log(len(treatedlist[0]))/log(2)) + print "n",n + l2n = range(int(pow(2,n))) + pi0 = [pow(2,-n) for _ in range(int(pow(2,n)))] + #treatedlist = [treatedlist[11]] + cpt = 0 + for perm in treatedlist: + M = np.zeros((pow(2,n),pow(2,n))) + for conf in l2n: + r = bin(perm[conf],n) + for cp in range(n): + confbp = bin(conf,n) + confbp[cp] = r[cp] + M[conf-1][dec(confbp,n)-1] = 1/float(n) + mx=0 + #print "Markov chain",M + eigs = np.linalg.eigvals(M) + #print "valp",eigs + error = 1E-10 + modulusofegs = [abs(l) for l in eigs] + modulusofegs = [l if (1-l)>error else 0 for l in modulusofegs] + #print "modulusofegs",modulusofegs + lambdastar = max(modulusofegs) + #print "lambdastar",lambdastar + trel = 1.0/(1-lambdastar) + def tmixSup(epsilon) : + pimin = 1.0/int(pow(2,n)) + #print "pimin",pimin + return np.log(1.0/(epsilon*pimin))*trel + def tmixInf(epsilon) : + pimin = 1.0/int(pow(2,n)) + #print "pimin",pimin + return (trel-1)*np.log(1.0/(2*epsilon)) + + + print "F_"+str(cpt+1), perm, int(tmixInf(epsilon)), int(tmixSup(epsilon))+1 + resTMIX +=[(perm, int(tmixInf(epsilon)), int(tmixSup(epsilon))+1)] + cpt+=1 + + def compare(x,y): + return cmp(x[1],y[1]) + resTMIX.sort(cmp=compare) + print resTMIX + + + +def is_double_stoc(M): + (nbl,nbc) =M.shape + return all( [abs (sum([M[i,j] for i in range(nbl)])-1.0)<1E-6 for j in range(nbc)]) + + + +def matriceAdjacenceDe(G): + l2n = range(int(pow(2,n))) + P = np.zeros((2**n,2**n)) + L = G.edges() + for i in l2n: + k = 0 + for j in l2n: + if i != j : + if (i,j) in L: + P[i][j] = 1/float(n) + k+=1 + P[i][i]=(n-k)/float(n) + return P + + +def graphe_OK(G): + M = matriceAdjacenceDe(G) + r = True + r = r and is_double_stoc(M) + r = r and nx.is_strongly_connected(G) + return r + + +def graphe_de_liste(l): + G = nx.DiGraph() + l2n = range(int(pow(2,n))) + for conf in l2n: + G.add_node(conf) + # r est l'image binaire de conf en parallele + r = bin(l[conf],n) + # on construit poentiellement les n image en unitaire + for cp in range(n): + # confbp est conf sauf en cp ou c'est r[cp] + confbp = bin(conf,n) + confbp[cp] = r[cp] + # on ajoute l'arc + G.add_edge(conf,dec(confbp,n)) + return G + + +acc={} +def genereGrapheHamiltonien(G): + global acc + def largeur(profondeur, effectues): + #print "profondeur",profondeur + global acc + effectues_p = [] + for (c,vi) in effectues: + (_,d) = c[len(c)-1] + for v in G.neighbors(d): + if v not in vi: + effectues_p += [([_ for _ in c]+[(d,v)],set([_ for _ in vi]+[v]))] + acc[profondeur] = effectues_p + if profondeur <= pow(2,n) : + largeur(profondeur+1,effectues_p) + largeur(4,[([(0,1)],set([0,1]))]) + res = acc[pow(2,n)+1] + ret=[] + for (c,vertices) in res : + assert len(vertices) == pow(2,n) + (_,t) = c[len(c)-1] + if G.has_edge(t,0) : + ret +=[c +[(t,0)]] + + return ret + + +def graphSansListe(G,l): + Gp = nx.DiGraph() + Gp.add_edges_from(G.edges()) + Gp.remove_edges_from(l) + return Gp + +def genereTousLesGraphesSansCycleHamiltonien(G): + r = [graphSansListe(G,l) for l in genereGrapheHamiltonien(G)] + res = [r[0]] + for g in r[1:] : + if all([not(isomorphic(g,g2)) for g2 in res]): + res.append(g) + return [grapheToList(G) for G in res] + +def graphe_de_edges(l): + G = nx.DiGraph() + l2n = range(int(pow(2,n))) + for conf in l2n: + G.add_node(conf) + for (o,e) in l: + G.add_edge(o,e) + return G + +# s'il y a des doublons ce n'est pas une perm +def isperm(L): + return len(set(L)) == len(L) + + +def grapheToList(G): + l2n = range(int(pow(2,n))) + edges = G.edges() + images = range(int(pow(2,n))) + for o in l2n: + e = o + eb= bin(e,n) + for j in range(n): + epb = bin(e,n) + epb[j] = 1-epb[j] + if (o,dec(epb,n)) in edges: + eb[j] = 1-eb[j] + images[o]=dec(eb,n) + return images + +def isomorphic(g1,g2): + GM = isomorphism.DiGraphMatcher(g1,g2) + return GM.is_isomorphic() + +def parcours_p(visited,resG,l): + + t = len(l) + for j in range(t): + lp = l[0:j]+l[j+1:] + G = graphe_de_edges(lp) + if nx.is_strongly_connected(G) : + if all([not(isomorphic(G,g2)) for g2 in visited]): + visited.append(G) + M = matriceAdjacenceDe(G) + if is_double_stoc(M): + resG.append(G) + gtl = grapheToList(G) + print gtl,len(resG) + parcours_p(visited,resG,G.edges()) + + +def parcours_l_dual(visited,resG,GGedges): + global prof + print "\n en entrant",int(prof),"a visiter",len(visited) + prof -=1 + nvisited =[] + for i in range(len(visited)) : + #if i%10 == 0 : + print "ds calcul",i,len(nvisited) + ld = visited[i].edges() + lr = list(GGedges-set(ld)) + + t = len(lr) + for j in range(t): + lp = [x for x in ld]+[lr[j]] + G= graphe_de_edges(list(GGedges-set(lp))) + if nx.is_strongly_connected(G) : + Gd= graphe_de_edges(lp) + if all([not(isomorphic(Gd,g2)) for g2 in nvisited]): + nvisited.append(Gd) + M = matriceAdjacenceDe(G) + if is_double_stoc(M): + resG.append(G) + gtl = grapheToList(G) + print "\n",gtl + if nvisited != [] : + parcours_l_dual(nvisited,resG,GGedges) + + +def parcours_l(visited,resG): + global prof + if prof < profM - nbmaxiter : + assert False + print "\n en entrant",int(prof),"a vistier",len(visited) + prof -=1 + nvisited =[] + for i in range(len(visited)) : + #if i%100 == 0 : + #print "ds calcul",i,len(nvisited) + l = visited[i].edges() + t = len(l) + for j in range(t): + lp = l[0:j]+l[j+1:] + G = graphe_de_edges(lp) + if nx.is_strongly_connected(G) : + if all([not(isomorphic(G,g2)) for g2 in nvisited]): + nvisited.append(G) + M = matriceAdjacenceDe(G) + if is_double_stoc(M): + resG.append(G) + gtl = grapheToList(G) + print "\n",gtl + if nvisited != [] : + parcours_l(nvisited,resG) + + + + + +def main(): + global treatedlist + l = range(int(pow(2,n))) + l.reverse() + G = graphe_de_liste(l) + treatedlist = genereTousLesGraphesSansCycleHamiltonien(G) + print treatedlist + #Ginit = nx.DiGraph() + #Ginit.add_edge(0,2) + #resG = [G] + # parcours en profondeur : deux graphes sont voinsin si l'un contient + # un arc de plus que l'autre + #visited=[] + #parcours_p(visited,resG,G.edges()) + #parcours_l([G],resG) + #parcours_l_dual([Ginit],resG,set(G.edges())) + + #print [grapheToList(X) for X in resG] + + + + + +def main_old(): + resl=[] + global treatedlist + if rf != False: + treatedlist =get_treatedlist(rf) + else : + treatedlist = [ perm for perm in permute_in_place(range(8))] + print "taillle de la liste ",len(treatedlist) + res = [] + resG= [] + global n + n= int(log(len(treatedlist[0]))/log(2)) + print "n",n + + nbit = 40 + + l2n = range(int(pow(2,n))) + # pour chaque permutation de l ensemble [0,...,2^[n-1}} + nnb = 0 + #for perm in permute_in_place(range(4)): + D=[0 for x in range(len(treatedlist))] + count=-1 + for perm in treatedlist: + count +=1 + nnb +=1 + #if nnb%1000 == 0 : + # print nnb + # si elle contient un element stable on l enleve (GTPIC n est pas SCC) + if all([ ident!=perm[ident] for ident in l2n]): + # on construit le GTPIC + #G = nx.DiGraph() + G = nx.DiGraph() + # pour chaque noeud + for conf in l2n: + G.add_node(conf) + # r est l'image binaire de conf en parallele + r = bin(perm[conf]) + # on construit poentiellement les n image en unitaire + for cp in range(n): + # confbp est conf sauf en cp ou c'est r[cp] + confbp = bin(conf) + confbp[cp] = r[cp] + # on ajoute l'arc + G.add_edge(conf,dec(confbp)) + flg = False + if nx.is_strongly_connected(G): + if len(resG)==0: + res.append(perm) + resG.append(G) + flg=True + else : + def isomorphic(g1,g2): + GM = isomorphism.DiGraphMatcher(g1,g2) + return GM.is_isomorphic() + if all([not(isomorphic(G,g2)) for g2 in resG]): + resG.append(G) + res.append(perm) + flg=True + #else: + # print "pas scc",perm + if flg == True : + T=[0 for i in l2n] + T[0] = 1 + P = np.zeros((2**n,2**n)) + for i in l2n: + k = 0 + for j in l2n: + L = G.edges() + if i != j : + if (i,j) in L: + P[i][j] = 1/float(n) + k+=1 + P[i][i]=(n-k)/float(n) + + + if is_double_stoc(P): + d=pow(2,n) + t=0 + unif = 1/float(pow(2,n)) + cpt=0 + while (d >0.00001 and t <10000): + cpt+=1 + #print cpt + T =[ sum ([T[j]*P[j][i] for j in l2n]) for i in l2n] + #print T + dp = sum([abs(x-unif) for x in T])*(pow(2,n)) + if dp < d : + D[count] = t + d = dp + t +=1 + #print dp + print perm, t, d, D[count] + resl +=[perm] + print resl + return resl +rf=False + +def options(): + global rf + parser = OptionParser() + parser.add_option("-i", "--input", dest="i", + help="file of sequences") + (options, args) = parser.parse_args() + if (options.i != None): + rf = options.i + + +if __name__ == "__main__": + options() + print "------" + main() + calculetmix(1E-4) + diff --git a/experiments/genHamiltonian.py b/experiments/genHamiltonian.py new file mode 100644 index 0000000..deefc04 --- /dev/null +++ b/experiments/genHamiltonian.py @@ -0,0 +1,279 @@ +import networkx as nx +from networkx.algorithms import isomorphism +from math import * +import numpy as np +from optparse import OptionParser +import random as rd +from copy import * +from combinaisons import * + + +# Implemantation of the balanced gray code algorithm,construction B +# detailled in "Totally Balanced and exponentially Balanced Gray codes", +# A J. van Zanten, I.N. Suparta 2004 + + + +def bin(elem,n): + """Convertit un nombre en binaire""" + q = -1 + res =[0 for i in range(n)] + i = 1 + while q != 0: + q = elem // 2 + r = elem % 2 + res[n-i] = r + elem = q + i+=1 + return res + +def dec(ch,n): + l = len(ch) + acc = 0 + for i in range(l): + if ch[i]==1: + acc = acc + 2**(n-i-1) + return acc + + +def flatten(x): + result = [] + for el in x: + if hasattr(el, "__iter__") and not isinstance(el, basestring): + result.extend(flatten(el)) + else: + result.append(el) + return result + + + +def genereToutesLesSousListes(n,su): + # specificique puisque la taille mini est 2 et commence par [0,1] + print "n",n,"su",su + r= [[0,1]] + for j in xrange(su-2): + print j + rp = [] + for li in r : + for el in range(li[-1]+1,n): + rp += [ li+[el]] + r= [x for x in rp] + return r + + + + + +def extraitSousListe(Snm2,sublisIndex,n): + #l is sublistdindices + nm2 = len(Snm2) + indexOfSnm2 = xrange(nm2) + # l is an even positive number + #assert l >= 0 and l%2 == 0 and l<= nm2 + l = len(sublisIndex) + #print "l",l,"n",n,"len(Snm2)",nm2 + # we have to select l elements, but the two first are always selected + #Silindex = [0,1]+rd.sample(xrange(2,nm2),l-2) + Silindex = sublisIndex + Silindex.sort() + Sil = [Snm2[x] for x in Silindex] + + dif = list(set(indexOfSnm2)-set(Silindex)) + dif.sort() + + Uinitial=[[]] + UinitialIndex = [[]] + cur = 2 + + for k in xrange(2,l): + Uinitial += [[Snm2[x] for x in range(cur,Silindex[k])]] + UinitialIndex = [[x for x in range(cur,Silindex[k])]] + cur = Silindex[k]+1 + v = [Snm2[x] for x in range(cur,nm2)] + + #print "Snm2",Snm2,"Silindex",Silindex,"Sil",Sil,"dif",dif,"Uinitial",Uinitial,"UinitialIndex",UinitialIndex,"v",v + return (Silindex,Sil,Uinitial,v) + + + + +def replace(Silindex,Sil,u,n,l,v): + def uExtended(u,j,n): + # If j is odd, we are in u(n-1,n), and u(n,n-1) otherwise + (X,Y) = (n-1,n) if i%2 == 1 else (n,n-1) + + uir = [_ for _ in u[i]] + uir.reverse() + R = [_ for _ in u[i]]+ [X] + uir + [Y] + [_ for _ in u[i]] + return R + + lu = len(u) + + Up = [n-1]+[uExtended(u,i,n) for i in range(1,lu)] + + U=[] + for j in xrange(l-2+1): + U += [Sil[j]] + U += [Up[j]] + U += [Sil[-1]] + U += v + return flatten(U) + + +def generateGrayCode(Snm2,sublistdindices): + + #Snm2 = [3,2,3,1,3,2,3,1] + n= int(log(len(Snm2))/log(2))+2 + l=int(pow(2,n)/n) + #step 1 + (Silindex,Sil,Uinitial,v) = extraitSousListe(Snm2,sublistdindices,n) + + + #step 2 : replace in Snm2 and genereate U + U = replace(Silindex,Sil,Uinitial,n,l,v) + + #step 3 : compute V and W + V = [_ for _ in v] + V.reverse() + V += [n] + [_ for _ in v] + W = [n-1] + [_ for _ in Snm2] +[n] + + #step 4 : swap value n-1 and s1 in W + Wp = [W[1]] + [n-1] + [_ for _ in W[2:]] + + #step 5 : generate Sn + Ur = [_ for _ in U] + Ur.reverse() + + Sn = Ur + V + Wp + return Sn + + +def is_totallyBalanced(l): + res = [0 for _ in range(max(l))] + for j in l : + res[j-1] +=1 + return (max(res) == min(res)) + +def is_onlyBalanced(l): + res = [0 for _ in range(max(l))] + for j in l : + res[j-1] +=1 + return max(res)- min(res) < 3 + + +def grapheToList(G,n): + l2n = range(int(pow(2,n))) + edges = G.edges() + images = range(int(pow(2,n))) + for o in l2n: + e = o + eb= bin(e,n) + for j in range(n): + epb = bin(e,n) + epb[j] = 1-epb[j] + if (o,dec(epb,n)) in edges: + eb[j] = 1-eb[j] + images[o]=dec(eb,n) + return images + + +def Sn2map(l): + n= int(log(len(l))/log(2)) + init = bin(0,n) + cheminb=[] + a = copy(init) + for i in l: + a[n-i] = 1 - a[n-i] + cheminb += [copy(a)] + chemin=[dec(x,n) for x in cheminb] + lc = len(chemin) + enl=[(chemin[i%lc],chemin[(i+1)%lc]) for i in range(lc)] + assert len(set(range(int(pow(2,n))))-set(chemin)) == 0 + # cheminp est le chemin hamiltonien correspondant a l + # on construit la fonction sans ce chemin hamiltonien + G = nx.DiGraph() + for i in range(2**n): + ib = bin(i,n) + for k in range(n): + ibp = [_ for _ in ib] + ibp[k]=1-ibp[k] + # si l'arrete ne doit pas etre enlevee + if (i,dec(ibp,n)) not in enl : + G.add_edge(i,dec(ibp,n)) + + #resl = grapheToList(G,n) + return (G,grapheToList(G,n)) + + + + + + +def main(): + snm2 = [[1,2,1,2]] + #snm2 = [[4, 5, 6, 2, 6, 5, 1, 5, 6, 2, 6, 5, 3, 5, 6, 1, 6, 5, 4, 5, 6, 1, 3, 2, 3, 4, 1, 4, 6, 4, 1, 4, 3, 2, 3, 5, 3, 2, 3, 4, 1, 4, 3, 5, 2, 6, 2, 5, 3, 4, 1, 4, 3, 2, 3, 1, 4, 1, 3, 2, 1, 2, 4, 6]] + resG=[] + p = 3 + for k in range(p): + print "taille de snm2", len(snm2) + snm2p = [] + for sn in snm2 : + n= int(log(len(sn))/log(2))+2 + ln= int(pow(2,n)/n) + #subls = genereToutesLesSousListes(int(pow(2,n-2)),ln) + #print "subls",subls + ll = range(int(pow(2,n-2))) + #for l in subls: + compteur = 0 + for l in xuniqueCombinations(ll[2:], ln-2): + compteur +=1 + l = [0,1]+l + nouveauCode = generateGrayCode(sn,l) + + + flg = False + + (G,nc) = Sn2map(nouveauCode) + #on verifie que la fonction est nouvelle + if nx.is_strongly_connected(G): + if len(resG)==0: + resG.append(G) + flg=True + else : + def isomorphic(g1,g2): + GM = isomorphism.DiGraphMatcher(g1,g2) + return GM.is_isomorphic() + if all([not(isomorphic(G,g2)) for g2 in resG]): + resG.append(G) + flg=True + if is_onlyBalanced(nouveauCode) : + snm2p +=[nouveauCode] + if is_totallyBalanced(nouveauCode) : + print "TB", nc + else : + print "OB", nc + snm2=deepcopy(snm2p) + + + + + + + +def options(): + global rf + parser = OptionParser() + parser.add_option("-i", "--input", dest="i", + help="file of sequences") + (options, args) = parser.parse_args() + if (options.i != None): + rf = options.i + + +if __name__ == "__main__": + options() + print "------" + main() + + diff --git a/experiments/genPrologFile.py b/experiments/genPrologFile.py new file mode 100644 index 0000000..c166ee9 --- /dev/null +++ b/experiments/genPrologFile.py @@ -0,0 +1,109 @@ + + + +n=2 +deuxExpN = pow(2,n) + + + +def bin(elem,n): + """Convertit un nombre en binaire""" + q = -1 + res =[0 for i in range(n)] + i = 1 + while q != 0: + q = elem // 2 + r = elem % 2 + res[n-i] = r + elem = q + i+=1 + return res + +def dec(ch,n): + l = len(ch) + acc = 0 + for i in range(l): + if ch[i]==1: + acc = acc + 2**(n-i-1) + return acc + + +def dist(i,j): + ib = bin(i,deuxExpN) + jb = bin(j,deuxExpN) + return sum([1 if ib[k] !=jb[k] else 0 for k in range(deuxExpN)]) + +st = "sc"+str(n)+"(X1):-\n" +for i in range(1,deuxExpN): + st += "\t mmult(X1,X"+str(i)+",X"+str(i+1)+"),\n" +st += "\t summ(X1,X2,S2),\n" +for i in range(2,deuxExpN): + st += "\t summ(S"+str(i)+",X"+str(i+1)+",S"+str(i+1)+"),\n" +st += "\t touspositifs(S"+str(deuxExpN)+").\n\n" + + + + +st += "bistoc(X):-\n" +# construction de X +X=[] +for i in range(deuxExpN): + XL=[] + for j in range(deuxExpN) : + XL.append('M'+str(i)+"X"+str(j)) + + X.append(XL) + + +st += "\t X=" +str(X).replace('\'','')+",\n" + +# domaine des variables +for i in range(deuxExpN): + for j in range(deuxExpN): + if dist(i,j)> 1 : + st += "\t M"+str(i)+"X"+str(j)+" is 0 ,\n" + else : + if i == j : + st += "\t M"+str(i)+"X"+str(j)+" in 0.."+str(n)+",\n" + else : + st += "\t M"+str(i)+"X"+str(j)+" in 0..1"+",\n" + +# stochastiques + +for i in range(deuxExpN): + stl ="" + for j in range(deuxExpN): + stl += "M"+str(i)+"X"+str(j) +"+ " + stl = stl[:-2] + st += "\t "+stl + " #="+str(n)+" ,\n" + + +# bistochastiques + +for i in range(deuxExpN): + stl,stlb ="","" + for j in range(deuxExpN): + stlb += "M"+str(j)+"X"+str(i) +"+ " + stlb = stlb[:-2] + st += "\t "+stlb + " #="+str(n)+" ,\n" + + +# label +lbl= [] +for i in range(deuxExpN): + for j in range(deuxExpN): + lbl.append('M'+str(i)+"X"+str(j)) + +st += "\t label("+ str(lbl).replace('\'','')+"),\n" + +st+= "\t sc"+str(n)+"(X), \n" +st+= "\t open('res"+str(n)+".txt',append,Stream),\n" +st+= "\t write(Stream,X),\n" +st+= "\t close(Stream).\n\n" + +print st + + +""" + sc2(X). +""" diff --git a/experiments/hamiltonien4.txt b/experiments/hamiltonien4.txt new file mode 100644 index 0000000..bbcc33f --- /dev/null +++ b/experiments/hamiltonien4.txt @@ -0,0 +1,15 @@ +------ +[[14, 6, 12, 4, 15, 11, 8, 10, 5, 7, 13, 0, 1, 3, 9, 2], [14, 6, 12, 4, 15, 8, 1, 9, 5, 7, 13, 0, 11, 10, 3, 2], [14, 6, 12, 4, 15, 8, 11, 9, 5, 7, 13, 0, 2, 10, 3, 1], [14, 6, 12, 4, 15, 2, 8, 10, 5, 7, 13, 0, 11, 3, 9, 1], [14, 6, 12, 4, 15, 11, 1, 9, 5, 7, 13, 0, 2, 10, 3, 8], [14, 6, 9, 8, 15, 11, 1, 10, 5, 7, 13, 12, 2, 0, 3, 4], [14, 6, 9, 4, 15, 11, 8, 12, 5, 7, 13, 0, 2, 10, 3, 1], [14, 6, 9, 13, 15, 2, 8, 10, 5, 7, 4, 12, 11, 0, 3, 1], [14, 6, 9, 13, 15, 11, 8, 0, 5, 7, 4, 12, 2, 10, 3, 1], [14, 6, 15, 8, 3, 11, 13, 10, 5, 7, 4, 12, 2, 0, 9, 1], [14, 6, 15, 8, 9, 11, 13, 0, 5, 7, 4, 12, 2, 10, 3, 1]] +n 4 +F_1 [14, 6, 12, 4, 15, 11, 8, 10, 5, 7, 13, 0, 1, 3, 9, 2] 18 39 +F_2 [14, 6, 12, 4, 15, 8, 1, 9, 5, 7, 13, 0, 11, 10, 3, 2] 15 34 +F_3 [14, 6, 12, 4, 15, 8, 11, 9, 5, 7, 13, 0, 2, 10, 3, 1] 15 34 +F_4 [14, 6, 12, 4, 15, 2, 8, 10, 5, 7, 13, 0, 11, 3, 9, 1] 20 41 +F_5 [14, 6, 12, 4, 15, 11, 1, 9, 5, 7, 13, 0, 2, 10, 3, 8] 13 32 +F_6 [14, 6, 9, 8, 15, 11, 1, 10, 5, 7, 13, 12, 2, 0, 3, 4] 13 32 +F_7 [14, 6, 9, 4, 15, 11, 8, 12, 5, 7, 13, 0, 2, 10, 3, 1] 15 34 +F_8 [14, 6, 9, 13, 15, 2, 8, 10, 5, 7, 4, 12, 11, 0, 3, 1] 15 34 +F_9 [14, 6, 9, 13, 15, 11, 8, 0, 5, 7, 4, 12, 2, 10, 3, 1] 18 38 +F_10 [14, 6, 15, 8, 3, 11, 13, 10, 5, 7, 4, 12, 2, 0, 9, 1] 13 32 +F_11 [14, 6, 15, 8, 9, 11, 13, 0, 5, 7, 4, 12, 2, 10, 3, 1] 16 36 +[([14, 6, 12, 4, 15, 11, 1, 9, 5, 7, 13, 0, 2, 10, 3, 8], 13, 32), ([14, 6, 9, 8, 15, 11, 1, 10, 5, 7, 13, 12, 2, 0, 3, 4], 13, 32), ([14, 6, 15, 8, 3, 11, 13, 10, 5, 7, 4, 12, 2, 0, 9, 1], 13, 32), ([14, 6, 12, 4, 15, 8, 1, 9, 5, 7, 13, 0, 11, 10, 3, 2], 15, 34), ([14, 6, 12, 4, 15, 8, 11, 9, 5, 7, 13, 0, 2, 10, 3, 1], 15, 34), ([14, 6, 9, 4, 15, 11, 8, 12, 5, 7, 13, 0, 2, 10, 3, 1], 15, 34), ([14, 6, 9, 13, 15, 2, 8, 10, 5, 7, 4, 12, 11, 0, 3, 1], 15, 34), ([14, 6, 15, 8, 9, 11, 13, 0, 5, 7, 4, 12, 2, 10, 3, 1], 16, 36), ([14, 6, 12, 4, 15, 11, 8, 10, 5, 7, 13, 0, 1, 3, 9, 2], 18, 39), ([14, 6, 9, 13, 15, 11, 8, 0, 5, 7, 4, 12, 2, 10, 3, 1], 18, 38), ([14, 6, 12, 4, 15, 2, 8, 10, 5, 7, 13, 0, 11, 3, 9, 1], 20, 41)] diff --git a/experiments/hamiltonien5.txt b/experiments/hamiltonien5.txt new file mode 100644 index 0000000..e69de29 diff --git a/experiments/mtrx.pl b/experiments/mtrx.pl new file mode 100644 index 0000000..f820f6c --- /dev/null +++ b/experiments/mtrx.pl @@ -0,0 +1,54 @@ +:-use_module(library(clpfd)). + + +% N is the dot product of lists V1 and V2. +dot(V1, V2, N) :- maplist(product,V1,V2,P), sumlist(P,N). +product(N1,N2,N3) :- N3 is N1*N2. + +% Matrix multiplication with matrices represented +% as lists of lists. M3 is the product of M1 and M2 +mmult(M1, M2, M3) :- transpose(M2,MT), maplist(mm_helper(MT), M1, M3). +mm_helper(M2, I1, M3) :- maplist(dot(I1), M2, M3). + + + + +suml([],[],[]). + +suml(L1,L2,[N|R2]):- + L1 = [E1|T1], + L2 = [E2|T2], + N is E1 + E2, + suml(T1,T2,R2). + + + +summ([],[],[]). +summ(M1,M2,[Lr|R2]):- + M1 = [E1|T1], + M2 = [E2|T2], + suml(E1,E2,Lr), + summ(T1,T2,R2). + + + +flatten(List, Flattened):- + flatten(List, [], Flattened). + +flatten([], Flattened, Flattened). +flatten([Item|Tail], L, Flattened):- + flatten(Item, L1, Flattened), + flatten(Tail, L, L1). +flatten(Item, Flattened, [Item|Flattened]):- + \+ is_list(Item). + +touspositifs(X):- + flatten(X,XF), + tp(XF). + +tp([]). +tp(X):- + X = [E|L], + E #>= 0, + tp(L). + diff --git a/experiments/prng.py b/experiments/prng.py new file mode 100644 index 0000000..0d6e0bc --- /dev/null +++ b/experiments/prng.py @@ -0,0 +1,108 @@ +from random import * +import numpy as np +from time import * +from math import * +from random import * + + + +# let elem be a integer. +# This function returns the binary value of elem +# expressed on n bits. +def bin(elem,n): + q = -1 + res =[0 for i in range(n)] + i = 1 + while q != 0: + q = elem // 2 + r = elem % 2 + res[n-i] = r + elem = q + i+=1 + return res + + +# let ch be a binary number expressed on n bits. +# This function returns the decimal value of this +# binary number. +def dec(ch,n): + l = len(ch) + acc = 0 + for i in range(l): + if ch[i]==1: + acc = acc + 2**(n-i-1) + return acc + + + +# Let be given a function f defined as a list of size 2^n +# that contains the images f[x] of the element at index x +# where x is an index, 0 <= x <= 2^n-1. +# Let X be an index, 0 <= x <= 2^n-1, and k be an index, 0 <= k <= n-1, +# this function returns the map fp such that fp[x][k] = y +# where y is x except at bit k where the value is the bit f[x][k]. +def f_to_map(f): + # size of + lf = len(f) + # number of bits + n= int(log(len(f))/log(2)) + # fp is the returned two dimensional array + fp = np.zeros((2**n,n)) + for i in xrange(lf): + ib = bin(i,n) + imgib = bin(f[i],n) + for j in xrange(n): + ibp = [_ for _ in ib] + ibp[j] = imgib[j] + fp[i,j] = dec(ibp,n) + return fp + + + +# let fmap be a function expressed as a map. +# let n be the largest value returned by the prng (i.e. the number of bits) +# let randf be a prng that can return integer from 0 to n-1 +# let b be the number of iterations +# le x0 be a integer value such that 0 <= x0 <= 2^n-1 +def ourPrng(fmap,n,randf,b,x0): + x = x0 + for _ in xrange(b): + s = randf(0,n-1) + x = fmap[x][s] + return x + + + +# Let be given a function f defined as a list of size N +# that contains the images f[x] of the element at index x and +# let b be the number of iterations that has to be executed and +# rand be a prng that can randomly find integer between two bounds. +# This function cumputes the NxN array successors such that +# successors[i][j] is the number of times i has been followed by j +# where 0 <= i <= N-1 and 0 <= j <= N-1. +def testPrng(f,rand,b): + lf = len(f) + successors=[[0 for _ in range(lf)] for _ in range(lf)] + x0 = 0 + fp = f_to_map(f) + n= int(log(len(f))/log(2)) + for _ in range(lf*lf*1000): + old_x = x0 + x0 = int(ourPrng(fp,n,rand,b,x0)) + successors[old_x][x0] +=1 + return successors + +def main(): + l1 = testPrng([13, 10, 9, 14, 3, 11, 1, 12, 15, 4, 7, 5, 2, 6, 0, 8],randint,32) + print l1 + l2 = testPrng([55, 60, 45, 56, 58, 62, 61, 40, 53, 38, 52, 54, 35, 51, 33, 49, 39, 14, 47, 46, 59, 43, 57, 44, 37, 6, 36, 4, 3, 50, 1, 48, 63, 26, 25, 30, 19, 27, 17, 28, 31, 20, 23, 21, 18, 22, 16, 24, 13, 12, 29, 8, 10, 42, 41, 0, 15, 2, 7, 5, 11, 34, 9, 32],randint,49) + print l2 + l3 = testPrng([223, 250, 249, 254, 187, 234, 241, 252, 183, 230, 229, 180, 227, 178, 240, 248, 237, 236, 253, 172, 251, 238, 201, 224, 247, 166, 165, 244, 163, 242, 161, 225, 215, 220, 205, 216, 218, 222, 221, 208, 213, 210, 212, 214, 219, 211, 217, 209, 239, 142, 207, 206, 139, 203, 193, 136, 135, 196, 199, 132, 194, 130, 129, 200, 159, 186, 185, 190, 59, 170, 177, 188, 191, 246, 245, 52, 243, 50, 176, 184, 173, 46, 189, 174, 235, 42, 233, 232, 231, 38, 37, 228, 35, 226, 33, 168, 151, 156, 141, 152, 154, 158, 157, 144, 149, 146, 148, 150, 155, 147, 153, 145, 175, 14, 143, 204, 11, 202, 169, 8, 7, 198, 197, 4, 195, 2, 1, 192, 255, 124, 109, 120, 107, 126, 125, 112, 103, 114, 116, 100, 123, 98, 121, 113, 79, 106, 111, 110, 75, 122, 97, 108, 71, 118, 117, 68, 115, 66, 96, 104, 127, 90, 89, 94, 83, 91, 81, 92, 95, 84, 87, 85, 82, 86, 80, 88, 77, 76, 93, 72, 74, 78, 105, 64, 69, 102, 101, 70, 99, 67, 73, 65, 55, 60, 45, 56, 51, 62, 61, 48, 119, 182, 181, 53, 179, 54, 57, 49, 15, 44, 47, 40, 171, 58, 9, 32, 167, 6, 5, 164, 3, 162, 41, 160, 63, 26, 25, 30, 19, 27, 17, 28, 31, 20, 23, 21, 18, 22, 16, 24, 13, 10, 29, 140, 43, 138, 137, 12, 39, 134, 133, 36, 131, 34, 0, 128],randint,75) + print l3 + + +if __name__ == "__main__": + main() + + + diff --git a/experiments/qian/analyseReport.py b/experiments/qian/analyseReport.py new file mode 100644 index 0000000..e0c27e9 --- /dev/null +++ b/experiments/qian/analyseReport.py @@ -0,0 +1,90 @@ +lf = ['finalAnalysisReport_jf_oldci_stable_b_4bit.txt', 'finalAnalysisReport_jf_oldci_stable_b_6bit.txt','finalAnalysisReport_jf_oldci_stable_b_8bit.txt'] + +lf = ['finalAnalysisReportFTTCS_4.txt'] + + +fd =[open(f,"r") for f in lf] + +lignes=[fdi.readlines()[7:] for fdi in fd] + +label = ["Frequency (Monobit)","Frequency within a Block","Runs","Longest Run of Ones in a Block","Binary Matrix Rank","Discrete Fourier Transform (Spectral)","Non-overlapping Template Matching*","Overlapping Template Matching","Maurer's \"Universal Statistical\"","Linear Complexity","Serial* (m=10)","Approximate Entropy (m=10)","Cumulative Sums (Cusum) *","Random Excursions *","Random Excursions Variant *"] + +endl="\\\\ \\hline \n" + + +st="" + +#freq + +def traitenlignes(num1,num2): + sti="" + for l in lignes: + #calcul des moyennes mv ms + mv,ms=0,0 + for j in range(num1,num2+1): + + stl=[] + for x in l[j].split(" "): + if x !='': + stl += [x] + + idxdiv = 0 + for i in range(len(stl)): + if stl[i].find('/') != -1: + idxdiv = i + mv += float(stl[idxdiv-1]) + rate = stl[idxdiv].split("/") + ms += float(rate[0])/float(rate[1]) + + #sti += "& " + str(mv/(num2-num1+1))[:5] + " (" + str(ms/(num2-num1+1))[0:5] +")" + sti += "& " + str(mv/(num2-num1+1))[:5] + "/" + str(round(100*ms/(num2-num1+1)))[0:2] + + return sti + endl + + + +def traite1ligne(numl): + sti="" + for l in lignes: + stl=[] + splitee = l[numl].split(" ") + for x in l[numl].split(" "): + if x !='': + stl += [x] + + idxdiv = 0 + for i in range(len(stl)): + #print splitee[i],i + if stl[i].find('/') != -1: + idxdiv = i + #print idxdiv + + r = str(round(float(stl[idxdiv].split("/")[0]))) + #ti += "& " + stl[idxdiv-1][:5] + " (" + r[0:5]+")" + sti += "& " + stl[idxdiv-1][:5] + "/" + r[0:2] + return sti + endl + +st += label[0] + traite1ligne(0) +st += label[1] + traite1ligne(1) +st += label[2] + traite1ligne(4) +st += label[3] + traite1ligne(5) +st += label[4] + traite1ligne(6) +st += label[5] + traite1ligne(7) +st += label[6] + traitenlignes(8,155) +st += label[7] + traite1ligne(156) +st += label[8] + traite1ligne(157) +st += label[9] + traite1ligne(185) +st += label[10] + traitenlignes(185,186) +st += label[11] + traite1ligne(187) +st += label[12] + traitenlignes(2,3) +st += label[13] + traitenlignes(159,166) +st += label[14] + traitenlignes(167,184) + + +print st + + + + + + diff --git a/experiments/qian/analyseReport.py~ b/experiments/qian/analyseReport.py~ new file mode 100644 index 0000000..081b1b2 --- /dev/null +++ b/experiments/qian/analyseReport.py~ @@ -0,0 +1,87 @@ +lf = ['finalAnalysisReport_jf_oldci_stable_b_4bit.txt', 'finalAnalysisReport_jf_oldci_stable_b_6bit.txt','finalAnalysisReport_jf_oldci_stable_b_8bit.txt'] + +fd =[open(f,"r") for f in lf] + +lignes=[fdi.readlines()[7:] for fdi in fd] + +label = ["Frequency (Monobit)","Frequency within a Block","Runs","Longest Run of Ones in a Block","Binary Matrix Rank","Discrete Fourier Transform (Spectral)","Non-overlapping Template Matching*","Overlapping Template Matching","Maurer's \"Universal Statistical\"","Linear Complexity","Serial* (m=10)","Approximate Entropy (m=10)","Cumulative Sums (Cusum) *","Random Excursions *","Random Excursions Variant *"] + +endl="\\\\ \\hline \n" + + +st="" + +#freq + +def traitenlignes(num1,num2): + sti="" + for l in lignes: + #calcul des moyennes mv ms + mv,ms=0,0 + for j in range(num1,num2+1): + + stl=[] + for x in l[j].split(" "): + if x !='': + stl += [x] + + idxdiv = 0 + for i in range(len(stl)): + if stl[i].find('/') != -1: + idxdiv = i + mv += float(stl[idxdiv-1]) + rate = stl[idxdiv].split("/") + ms += float(rate[0])/float(rate[1]) + + #sti += "& " + str(mv/(num2-num1+1))[:5] + " (" + str(ms/(num2-num1+1))[0:5] +")" + sti += "& " + str(mv/(num2-num1+1))[:5] + "/" + str(round(100*ms/(num2-num1+1)))[0:2] + + return sti + endl + + + +def traite1ligne(numl): + sti="" + for l in lignes: + stl=[] + splitee = l[numl].split(" ") + for x in l[numl].split(" "): + if x !='': + stl += [x] + + idxdiv = 0 + for i in range(len(stl)): + #print splitee[i],i + if stl[i].find('/') != -1: + idxdiv = i + #print idxdiv + + r = str(round(float(stl[idxdiv].split("/")[0]))) + #ti += "& " + stl[idxdiv-1][:5] + " (" + r[0:5]+")" + sti += "& " + stl[idxdiv-1][:5] + "/" + r[0:2] + return sti + endl + +st += label[0] + traite1ligne(0) +st += label[1] + traite1ligne(1) +st += label[2] + traite1ligne(4) +st += label[3] + traite1ligne(5) +st += label[4] + traite1ligne(6) +st += label[5] + traite1ligne(7) +st += label[6] + traitenlignes(8,155) +st += label[7] + traite1ligne(156) +st += label[8] + traite1ligne(157) +st += label[9] + traite1ligne(185) +st += label[10] + traitenlignes(185,186) +st += label[11] + traite1ligne(187) +st += label[12] + traitenlignes(2,3) +st += label[13] + traitenlignes(159,166) +st += label[14] + traitenlignes(167,184) + + +print st + + + + + + diff --git a/experiments/qian/finalAnalysisReportFTTCS_4.txt b/experiments/qian/finalAnalysisReportFTTCS_4.txt new file mode 100644 index 0000000..d72aca9 --- /dev/null +++ b/experiments/qian/finalAnalysisReportFTTCS_4.txt @@ -0,0 +1,208 @@ +------------------------------------------------------------------------------ +RESULTS FOR THE UNIFORMITY OF P-VALUES AND THE PROPORTION OF PASSING SEQUENCES +------------------------------------------------------------------------------ + generator is +------------------------------------------------------------------------------ + C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 P-VALUE PROPORTION STATISTICAL TEST +------------------------------------------------------------------------------ + 6 10 9 14 6 10 15 8 10 12 0.514124 99/100 Frequency + 10 14 8 17 12 7 9 10 7 6 0.289667 98/100 BlockFrequency + 11 10 10 8 9 6 9 19 8 10 0.289667 98/100 CumulativeSums + 8 7 14 8 10 15 10 8 11 9 0.699313 99/100 CumulativeSums + 9 11 18 9 7 7 10 7 7 15 0.171867 100/100 Runs + 10 15 11 10 15 10 6 14 3 6 0.096578 99/100 LongestRun + 6 11 12 8 9 12 12 6 11 13 0.739918 100/100 Rank + 13 9 13 4 9 9 14 11 11 7 0.494392 98/100 FFT + 7 7 10 16 15 16 11 6 7 5 0.055361 100/100 NonOverlappingTemplate + 7 10 12 10 7 5 19 7 11 12 0.115387 99/100 NonOverlappingTemplate + 9 8 16 13 9 9 12 7 9 8 0.637119 99/100 NonOverlappingTemplate + 9 9 11 10 11 4 16 12 9 9 0.514124 99/100 NonOverlappingTemplate + 8 11 9 12 10 9 8 13 6 14 0.779188 98/100 NonOverlappingTemplate + 6 10 11 9 8 9 11 11 13 12 0.924076 100/100 NonOverlappingTemplate + 12 6 9 14 6 7 12 12 16 6 0.202268 97/100 NonOverlappingTemplate + 9 16 15 7 14 5 13 6 10 5 0.062821 100/100 NonOverlappingTemplate + 14 7 9 13 7 10 9 11 8 12 0.798139 97/100 NonOverlappingTemplate + 12 10 6 11 14 11 11 11 6 8 0.739918 100/100 NonOverlappingTemplate + 12 9 6 9 14 12 5 12 11 10 0.616305 98/100 NonOverlappingTemplate + 12 8 12 13 10 8 8 8 8 13 0.867692 99/100 NonOverlappingTemplate + 15 18 7 11 12 7 6 8 10 6 0.096578 100/100 NonOverlappingTemplate + 13 5 9 12 8 15 12 6 9 11 0.437274 100/100 NonOverlappingTemplate + 9 13 10 12 9 14 4 11 9 9 0.637119 100/100 NonOverlappingTemplate + 11 17 10 11 10 6 8 12 9 6 0.419021 99/100 NonOverlappingTemplate + 11 7 15 6 6 6 9 8 15 17 0.062821 100/100 NonOverlappingTemplate + 5 9 12 6 12 18 5 10 10 13 0.096578 99/100 NonOverlappingTemplate + 3 16 6 10 8 8 11 11 11 16 0.096578 100/100 NonOverlappingTemplate + 9 8 5 11 7 8 14 13 17 8 0.202268 100/100 NonOverlappingTemplate + 7 7 13 16 3 11 17 6 8 12 0.028817 100/100 NonOverlappingTemplate + 9 5 19 16 5 10 5 3 16 12 0.000883 99/100 NonOverlappingTemplate + 8 6 8 13 17 9 11 10 12 6 0.319084 100/100 NonOverlappingTemplate + 9 13 11 10 11 9 11 13 6 7 0.851383 100/100 NonOverlappingTemplate + 8 9 12 9 10 9 19 10 7 7 0.275709 100/100 NonOverlappingTemplate + 17 9 11 9 6 12 11 11 11 3 0.191687 99/100 NonOverlappingTemplate + 10 10 10 10 9 13 9 11 9 9 0.997823 98/100 NonOverlappingTemplate + 12 11 5 9 13 9 13 12 10 6 0.637119 98/100 NonOverlappingTemplate + 11 11 7 9 14 11 11 10 5 11 0.779188 98/100 NonOverlappingTemplate + 7 8 11 9 8 10 15 17 9 6 0.275709 100/100 NonOverlappingTemplate + 6 6 9 11 13 17 12 9 11 6 0.249284 99/100 NonOverlappingTemplate + 11 8 12 13 5 12 12 10 9 8 0.779188 99/100 NonOverlappingTemplate + 11 2 8 9 8 10 11 15 11 15 0.181557 98/100 NonOverlappingTemplate + 8 11 10 9 10 14 7 14 8 9 0.816537 100/100 NonOverlappingTemplate + 9 8 9 10 10 13 12 13 11 5 0.798139 99/100 NonOverlappingTemplate + 10 10 10 7 13 10 10 8 12 10 0.978072 99/100 NonOverlappingTemplate + 11 11 10 12 8 10 8 10 9 11 0.996335 98/100 NonOverlappingTemplate + 9 13 13 10 6 10 6 8 13 12 0.657933 99/100 NonOverlappingTemplate + 11 13 5 10 8 17 13 9 8 6 0.224821 98/100 NonOverlappingTemplate + 7 12 12 6 10 13 7 9 14 10 0.657933 100/100 NonOverlappingTemplate + 8 14 9 10 6 12 6 13 8 14 0.474986 98/100 NonOverlappingTemplate + 12 8 3 11 14 12 11 8 17 4 0.051942 98/100 NonOverlappingTemplate + 10 8 11 13 5 5 16 12 11 9 0.304126 99/100 NonOverlappingTemplate + 10 13 11 13 9 7 13 10 7 7 0.779188 98/100 NonOverlappingTemplate + 11 7 11 14 8 11 12 7 7 12 0.759756 99/100 NonOverlappingTemplate + 15 13 7 8 8 6 16 7 6 14 0.108791 99/100 NonOverlappingTemplate + 14 7 12 6 10 8 8 6 11 18 0.145326 99/100 NonOverlappingTemplate + 14 8 8 14 11 11 9 6 8 11 0.699313 98/100 NonOverlappingTemplate + 12 13 15 8 5 9 6 15 11 6 0.181557 99/100 NonOverlappingTemplate + 12 10 11 14 7 11 13 8 5 9 0.637119 99/100 NonOverlappingTemplate + 13 8 7 11 9 12 8 11 10 11 0.946308 99/100 NonOverlappingTemplate + 10 6 7 6 10 10 12 14 14 11 0.554420 100/100 NonOverlappingTemplate + 12 13 4 14 8 12 12 6 9 10 0.401199 100/100 NonOverlappingTemplate + 8 10 5 13 9 8 14 16 7 10 0.319084 99/100 NonOverlappingTemplate + 12 7 16 11 9 12 3 9 11 10 0.304126 98/100 NonOverlappingTemplate + 16 6 13 10 7 11 6 8 8 15 0.213309 100/100 NonOverlappingTemplate + 12 12 6 10 11 13 11 4 9 12 0.574903 99/100 NonOverlappingTemplate + 6 11 10 12 8 13 9 12 9 10 0.911413 100/100 NonOverlappingTemplate + 6 10 10 10 7 7 15 14 10 11 0.574903 99/100 NonOverlappingTemplate + 7 10 11 8 5 10 10 16 12 11 0.534146 100/100 NonOverlappingTemplate + 9 8 7 14 7 14 11 10 8 12 0.699313 98/100 NonOverlappingTemplate + 7 7 14 15 12 10 13 10 7 5 0.304126 100/100 NonOverlappingTemplate + 8 9 12 6 6 13 12 12 7 15 0.419021 99/100 NonOverlappingTemplate + 11 13 8 11 8 10 9 8 14 8 0.883171 99/100 NonOverlappingTemplate + 10 7 13 9 10 9 11 12 10 9 0.978072 100/100 NonOverlappingTemplate + 5 9 3 11 12 8 19 7 12 14 0.021999 98/100 NonOverlappingTemplate + 10 10 7 7 9 16 10 12 7 12 0.616305 100/100 NonOverlappingTemplate + 6 6 8 15 3 10 10 17 16 9 0.020548 100/100 NonOverlappingTemplate + 13 8 11 10 7 10 7 10 9 15 0.759756 100/100 NonOverlappingTemplate + 11 7 9 6 14 6 17 11 8 11 0.249284 97/100 NonOverlappingTemplate + 7 9 14 10 4 17 8 11 9 11 0.224821 100/100 NonOverlappingTemplate + 11 9 8 14 14 3 7 6 13 15 0.102526 96/100 NonOverlappingTemplate + 14 6 11 12 11 6 9 14 9 8 0.574903 100/100 NonOverlappingTemplate + 10 10 8 11 12 12 4 10 11 12 0.798139 100/100 NonOverlappingTemplate + 7 7 10 16 15 16 11 6 7 5 0.055361 100/100 NonOverlappingTemplate + 13 11 10 8 10 13 9 11 11 4 0.719747 99/100 NonOverlappingTemplate + 10 14 4 9 10 13 13 11 11 5 0.366918 100/100 NonOverlappingTemplate + 16 5 8 11 10 14 8 9 10 9 0.455937 97/100 NonOverlappingTemplate + 18 10 12 12 8 8 3 11 13 5 0.058984 99/100 NonOverlappingTemplate + 13 9 5 12 16 6 14 8 5 12 0.122325 98/100 NonOverlappingTemplate + 4 4 13 11 12 8 9 16 12 11 0.153763 100/100 NonOverlappingTemplate + 9 2 10 8 9 16 13 14 12 7 0.108791 97/100 NonOverlappingTemplate + 5 14 10 13 10 5 14 9 7 13 0.275709 100/100 NonOverlappingTemplate + 10 9 8 6 13 11 10 14 4 15 0.289667 100/100 NonOverlappingTemplate + 14 12 5 12 9 11 11 5 10 11 0.554420 99/100 NonOverlappingTemplate + 4 7 16 7 12 12 11 14 7 10 0.191687 99/100 NonOverlappingTemplate + 7 7 7 12 14 12 9 12 6 14 0.455937 100/100 NonOverlappingTemplate + 12 14 6 15 6 8 13 10 10 6 0.304126 98/100 NonOverlappingTemplate + 3 10 11 8 11 6 9 9 15 18 0.062821 100/100 NonOverlappingTemplate + 8 10 9 13 11 7 6 14 10 12 0.739918 98/100 NonOverlappingTemplate + 8 5 8 13 10 9 10 8 13 16 0.419021 98/100 NonOverlappingTemplate + 11 11 11 10 13 12 8 8 7 9 0.946308 100/100 NonOverlappingTemplate + 14 7 8 9 13 6 5 12 14 12 0.319084 98/100 NonOverlappingTemplate + 18 8 10 9 12 1 7 13 12 10 0.040108 97/100 NonOverlappingTemplate + 12 7 9 10 10 8 11 8 10 15 0.851383 99/100 NonOverlappingTemplate + 14 8 7 10 3 8 11 12 8 19 0.045675 97/100 NonOverlappingTemplate + 10 11 6 10 14 10 3 10 11 15 0.289667 99/100 NonOverlappingTemplate + 13 12 11 7 7 11 10 11 9 9 0.935716 100/100 NonOverlappingTemplate + 14 6 7 11 14 9 10 13 8 8 0.574903 100/100 NonOverlappingTemplate + 8 6 10 10 6 9 12 14 5 20 0.032923 100/100 NonOverlappingTemplate + 16 9 10 8 8 11 8 6 13 11 0.574903 99/100 NonOverlappingTemplate + 8 11 11 5 13 9 11 10 12 10 0.867692 97/100 NonOverlappingTemplate + 9 9 6 16 10 10 6 14 10 10 0.474986 100/100 NonOverlappingTemplate + 13 11 9 10 12 12 7 6 16 4 0.236810 99/100 NonOverlappingTemplate + 12 6 9 14 14 11 9 13 9 3 0.249284 97/100 NonOverlappingTemplate + 9 9 13 13 6 10 8 8 13 11 0.798139 99/100 NonOverlappingTemplate + 9 10 9 5 10 7 8 14 13 15 0.437274 100/100 NonOverlappingTemplate + 13 11 13 6 11 5 13 11 8 9 0.574903 98/100 NonOverlappingTemplate + 13 15 7 11 10 6 12 8 7 11 0.554420 100/100 NonOverlappingTemplate + 11 9 11 15 9 7 12 10 8 8 0.834308 98/100 NonOverlappingTemplate + 7 5 12 13 6 7 14 20 7 9 0.019188 99/100 NonOverlappingTemplate + 7 7 10 19 11 8 7 14 9 8 0.145326 99/100 NonOverlappingTemplate + 7 7 14 12 7 12 6 12 10 13 0.534146 99/100 NonOverlappingTemplate + 16 10 8 9 8 16 8 6 11 8 0.304126 98/100 NonOverlappingTemplate + 10 9 8 8 10 9 11 19 8 8 0.350485 98/100 NonOverlappingTemplate + 7 11 11 10 8 10 9 11 13 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9 16 0.153763 99/100 NonOverlappingTemplate + 7 11 7 12 7 12 12 8 10 14 0.739918 100/100 NonOverlappingTemplate + 7 10 8 15 12 12 13 8 9 6 0.574903 99/100 NonOverlappingTemplate + 6 9 11 13 10 9 19 8 8 7 0.181557 100/100 NonOverlappingTemplate + 8 4 17 11 11 10 10 12 9 8 0.350485 99/100 NonOverlappingTemplate + 13 10 9 12 7 9 10 8 13 9 0.924076 99/100 NonOverlappingTemplate + 10 8 13 11 9 6 9 5 16 13 0.334538 99/100 NonOverlappingTemplate + 8 9 12 14 8 12 7 10 10 10 0.897763 100/100 NonOverlappingTemplate + 10 8 7 9 9 13 15 11 7 11 0.739918 100/100 NonOverlappingTemplate + 6 14 13 10 8 10 11 9 10 9 0.851383 99/100 NonOverlappingTemplate + 8 12 12 9 9 9 11 7 13 10 0.946308 99/100 NonOverlappingTemplate + 10 10 11 10 12 5 13 11 8 10 0.883171 100/100 NonOverlappingTemplate + 7 9 12 14 11 14 10 11 7 5 0.514124 100/100 NonOverlappingTemplate + 8 12 10 11 10 8 15 6 14 6 0.474986 99/100 NonOverlappingTemplate + 10 9 11 8 8 9 12 11 7 15 0.834308 100/100 NonOverlappingTemplate + 13 11 10 10 9 11 9 3 16 8 0.334538 100/100 NonOverlappingTemplate + 6 11 6 15 9 13 13 10 8 9 0.514124 100/100 NonOverlappingTemplate + 10 10 8 11 12 12 4 10 11 12 0.798139 100/100 NonOverlappingTemplate + 12 6 12 6 12 12 11 10 12 7 0.719747 99/100 OverlappingTemplate + 12 14 9 10 10 5 13 7 13 7 0.514124 100/100 Universal + 16 14 12 7 9 7 3 11 12 9 0.162606 96/100 ApproximateEntropy + 2 5 7 6 6 6 5 11 2 5 0.202268 55/55 RandomExcursions + 2 5 8 6 1 3 8 5 6 11 0.048716 55/55 RandomExcursions + 4 7 4 8 7 6 2 6 6 5 0.719747 55/55 RandomExcursions + 6 7 7 4 10 5 1 5 6 4 0.304126 55/55 RandomExcursions + 3 4 6 6 4 8 10 3 7 4 0.334538 55/55 RandomExcursions + 4 5 6 6 5 9 7 5 4 4 0.834308 55/55 RandomExcursions + 6 1 10 5 2 8 7 3 5 8 0.080519 53/55 RandomExcursions + 4 8 5 9 3 4 5 7 6 4 0.595549 53/55 RandomExcursions + 6 5 7 3 5 3 8 4 6 8 0.678686 55/55 RandomExcursionsVariant + 4 6 6 5 6 2 8 5 9 4 0.554420 55/55 RandomExcursionsVariant + 6 3 6 2 9 6 5 8 4 6 0.474986 55/55 RandomExcursionsVariant + 6 5 5 2 11 4 7 2 8 5 0.129620 55/55 RandomExcursionsVariant + 7 5 4 4 7 9 8 4 3 4 0.514124 55/55 RandomExcursionsVariant + 6 6 5 3 3 9 11 2 8 2 0.037566 55/55 RandomExcursionsVariant + 6 4 6 3 4 7 6 5 7 7 0.897763 55/55 RandomExcursionsVariant + 7 4 5 6 4 3 7 2 6 11 0.202268 55/55 RandomExcursionsVariant + 4 10 4 3 5 5 2 5 10 7 0.129620 54/55 RandomExcursionsVariant + 3 5 8 6 5 8 6 5 4 5 0.834308 55/55 RandomExcursionsVariant + 1 13 7 5 6 2 6 4 8 3 0.009535 55/55 RandomExcursionsVariant + 2 9 12 4 6 5 5 4 3 5 0.062821 55/55 RandomExcursionsVariant + 4 6 11 9 4 4 3 4 6 4 0.181557 55/55 RandomExcursionsVariant + 5 9 10 7 1 5 3 5 7 3 0.102526 55/55 RandomExcursionsVariant + 7 7 8 7 4 3 8 3 5 3 0.474986 55/55 RandomExcursionsVariant + 7 9 5 2 9 6 5 4 6 2 0.249284 55/55 RandomExcursionsVariant + 7 9 5 3 6 4 5 8 6 2 0.437274 54/55 RandomExcursionsVariant + 7 7 6 3 4 6 5 3 9 5 0.637119 55/55 RandomExcursionsVariant + 5 9 8 19 15 9 14 8 7 6 0.032923 100/100 Serial + 5 10 7 14 14 9 10 11 11 9 0.637119 100/100 Serial + 11 8 14 7 8 13 9 12 9 9 0.834308 98/100 LinearComplexity + + +- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - +The minimum pass rate for each statistical test with the exception of the +random excursion (variant) test is approximately = 96 for a +sample size = 100 binary sequences. + +The minimum pass rate for the random excursion (variant) test +is approximately = 52 for a sample size = 55 binary sequences. + +For further guidelines construct a probability table using the MAPLE program +provided in the addendum section of the documentation. +- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - diff --git a/experiments/qian/finalAnalysisReport_jf_oldci_stable_b_4bit.txt b/experiments/qian/finalAnalysisReport_jf_oldci_stable_b_4bit.txt new file mode 100644 index 0000000..a482892 --- /dev/null +++ b/experiments/qian/finalAnalysisReport_jf_oldci_stable_b_4bit.txt @@ -0,0 +1,208 @@ +------------------------------------------------------------------------------ +RESULTS FOR THE UNIFORMITY OF P-VALUES AND THE PROPORTION OF PASSING SEQUENCES +------------------------------------------------------------------------------ + generator is +------------------------------------------------------------------------------ + C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 P-VALUE PROPORTION STATISTICAL TEST +------------------------------------------------------------------------------ + 9 10 10 6 13 9 9 15 7 12 0.678686 99/100 Frequency + 12 5 8 16 5 15 6 13 11 9 0.102526 99/100 BlockFrequency + 9 8 5 12 11 12 9 14 9 11 0.759756 99/100 CumulativeSums + 9 7 13 12 5 6 10 15 11 12 0.401199 99/100 CumulativeSums + 12 12 10 6 12 5 17 5 10 11 0.171867 98/100 Runs + 9 12 13 7 4 9 11 11 6 18 0.115387 98/100 LongestRun + 10 6 11 9 14 11 7 13 14 5 0.401199 97/100 Rank + 14 12 10 10 13 8 8 12 9 4 0.554420 98/100 FFT + 8 9 9 10 14 10 10 16 6 8 0.554420 100/100 NonOverlappingTemplate + 7 10 12 10 2 13 8 5 17 16 0.017912 100/100 NonOverlappingTemplate + 9 8 12 11 10 13 8 7 12 10 0.935716 98/100 NonOverlappingTemplate + 8 15 11 6 5 8 7 13 12 15 0.202268 100/100 NonOverlappingTemplate + 12 14 10 7 8 7 16 6 10 10 0.401199 99/100 NonOverlappingTemplate + 12 11 12 11 11 7 13 5 9 9 0.779188 99/100 NonOverlappingTemplate + 12 13 10 7 3 9 11 13 10 12 0.474986 96/100 NonOverlappingTemplate + 9 12 11 6 11 11 11 12 7 10 0.924076 98/100 NonOverlappingTemplate + 9 10 11 12 9 11 12 7 13 6 0.867692 99/100 NonOverlappingTemplate + 10 10 8 10 11 6 17 16 6 6 0.129620 99/100 NonOverlappingTemplate + 11 8 16 13 6 2 8 11 9 16 0.045675 98/100 NonOverlappingTemplate + 7 12 14 10 15 8 11 5 8 10 0.455937 100/100 NonOverlappingTemplate + 15 7 12 14 10 11 9 6 12 4 0.262249 99/100 NonOverlappingTemplate + 8 10 9 13 11 8 14 11 13 3 0.401199 99/100 NonOverlappingTemplate + 8 9 7 22 9 8 4 11 10 12 0.015598 99/100 NonOverlappingTemplate + 9 7 6 14 11 14 16 8 8 7 0.262249 99/100 NonOverlappingTemplate + 7 10 6 11 14 12 12 11 5 12 0.534146 99/100 NonOverlappingTemplate + 7 14 7 14 7 8 17 8 9 9 0.224821 100/100 NonOverlappingTemplate + 8 12 9 9 7 10 12 14 11 8 0.883171 100/100 NonOverlappingTemplate + 11 8 6 12 10 8 12 14 9 10 0.834308 100/100 NonOverlappingTemplate + 10 10 11 14 13 8 11 7 7 9 0.834308 100/100 NonOverlappingTemplate + 8 7 8 14 6 7 17 8 17 8 0.058984 98/100 NonOverlappingTemplate + 12 10 8 8 6 9 10 11 11 15 0.779188 98/100 NonOverlappingTemplate + 8 7 11 9 11 12 10 10 12 10 0.983453 100/100 NonOverlappingTemplate + 17 8 6 10 7 10 11 8 12 11 0.455937 96/100 NonOverlappingTemplate + 8 6 16 8 10 10 12 11 9 10 0.678686 99/100 NonOverlappingTemplate + 9 11 8 5 14 13 11 8 13 8 0.595549 99/100 NonOverlappingTemplate + 9 13 9 10 4 10 14 8 13 10 0.574903 98/100 NonOverlappingTemplate + 8 9 17 7 7 12 4 10 11 15 0.129620 100/100 NonOverlappingTemplate + 6 5 11 7 13 6 14 11 5 22 0.001895 99/100 NonOverlappingTemplate + 10 7 12 6 10 10 9 10 12 14 0.834308 99/100 NonOverlappingTemplate + 8 14 13 8 13 9 10 7 9 9 0.798139 99/100 NonOverlappingTemplate + 5 9 15 9 11 8 10 12 9 12 0.678686 100/100 NonOverlappingTemplate + 5 9 12 8 12 9 18 8 9 10 0.289667 98/100 NonOverlappingTemplate + 10 5 5 6 9 15 14 12 12 12 0.213309 98/100 NonOverlappingTemplate + 6 14 10 12 5 14 7 11 12 9 0.419021 100/100 NonOverlappingTemplate + 7 15 5 7 12 15 9 9 11 10 0.350485 100/100 NonOverlappingTemplate + 9 16 10 7 12 8 12 9 9 8 0.699313 99/100 NonOverlappingTemplate + 10 13 14 6 9 9 10 9 9 11 0.867692 98/100 NonOverlappingTemplate + 11 13 8 11 5 7 11 11 9 14 0.657933 99/100 NonOverlappingTemplate + 10 15 11 8 12 9 9 11 9 6 0.798139 100/100 NonOverlappingTemplate + 10 8 15 9 7 12 7 12 11 9 0.759756 100/100 NonOverlappingTemplate + 11 12 10 11 13 10 8 13 9 3 0.554420 98/100 NonOverlappingTemplate + 16 7 8 12 13 12 10 3 14 5 0.075719 100/100 NonOverlappingTemplate + 15 11 15 9 14 3 6 8 12 7 0.090936 100/100 NonOverlappingTemplate + 9 8 6 7 11 9 10 13 11 16 0.554420 98/100 NonOverlappingTemplate + 14 5 7 7 10 12 13 7 14 11 0.366918 97/100 NonOverlappingTemplate + 7 7 15 10 14 6 10 9 8 14 0.383827 99/100 NonOverlappingTemplate + 9 9 13 12 8 10 11 7 11 10 0.964295 99/100 NonOverlappingTemplate + 5 17 6 16 5 6 12 14 10 9 0.026948 100/100 NonOverlappingTemplate + 6 12 9 10 11 8 9 8 15 12 0.739918 99/100 NonOverlappingTemplate + 3 13 7 12 8 6 8 13 11 19 0.028817 100/100 NonOverlappingTemplate + 6 12 10 10 11 12 11 10 9 9 0.971699 98/100 NonOverlappingTemplate + 12 14 8 13 9 8 7 11 8 10 0.816537 99/100 NonOverlappingTemplate + 13 14 8 8 9 9 8 12 9 10 0.883171 99/100 NonOverlappingTemplate + 11 10 9 12 10 12 6 14 5 11 0.657933 99/100 NonOverlappingTemplate + 8 7 11 5 14 15 11 9 12 8 0.437274 99/100 NonOverlappingTemplate + 6 11 10 12 12 12 11 10 7 9 0.911413 100/100 NonOverlappingTemplate + 8 7 9 9 13 5 13 12 9 15 0.455937 99/100 NonOverlappingTemplate + 10 6 11 12 6 11 10 13 10 11 0.851383 100/100 NonOverlappingTemplate + 15 6 13 11 14 9 7 9 10 6 0.401199 97/100 NonOverlappingTemplate + 5 7 13 11 14 9 12 10 13 6 0.437274 100/100 NonOverlappingTemplate + 12 10 7 7 8 10 11 16 13 6 0.455937 100/100 NonOverlappingTemplate + 10 9 11 5 9 18 11 8 8 11 0.334538 100/100 NonOverlappingTemplate + 11 10 9 9 16 12 9 6 10 8 0.699313 99/100 NonOverlappingTemplate + 8 9 8 8 12 9 11 15 10 10 0.883171 100/100 NonOverlappingTemplate + 9 7 14 10 16 10 7 17 5 5 0.048716 99/100 NonOverlappingTemplate + 6 14 8 13 8 11 15 7 10 8 0.455937 100/100 NonOverlappingTemplate + 8 9 13 10 7 11 11 9 13 9 0.935716 100/100 NonOverlappingTemplate + 11 12 11 8 10 13 4 13 7 11 0.595549 99/100 NonOverlappingTemplate + 16 7 14 8 8 5 10 12 11 9 0.350485 96/100 NonOverlappingTemplate + 7 5 9 8 7 11 11 13 15 14 0.350485 99/100 NonOverlappingTemplate + 7 14 10 16 9 8 7 8 9 12 0.494392 98/100 NonOverlappingTemplate + 10 8 9 14 8 11 8 9 9 14 0.851383 100/100 NonOverlappingTemplate + 8 9 9 10 14 10 10 16 6 8 0.554420 100/100 NonOverlappingTemplate + 17 6 9 9 12 10 7 7 14 9 0.304126 98/100 NonOverlappingTemplate + 7 15 8 6 8 9 14 10 14 9 0.419021 98/100 NonOverlappingTemplate + 12 10 12 10 13 6 4 12 11 10 0.595549 100/100 NonOverlappingTemplate + 13 11 10 7 13 7 11 14 7 7 0.616305 98/100 NonOverlappingTemplate + 5 16 10 8 10 13 13 10 10 5 0.289667 99/100 NonOverlappingTemplate + 6 12 8 13 9 15 10 8 11 8 0.657933 98/100 NonOverlappingTemplate + 11 11 11 10 9 14 12 4 7 11 0.637119 97/100 NonOverlappingTemplate + 9 7 9 6 11 9 12 15 10 12 0.719747 99/100 NonOverlappingTemplate + 20 8 16 6 7 4 11 13 9 6 0.006661 98/100 NonOverlappingTemplate + 11 10 10 12 8 9 10 9 11 10 0.998821 99/100 NonOverlappingTemplate + 7 11 9 10 10 5 11 15 13 9 0.616305 98/100 NonOverlappingTemplate + 11 12 14 10 11 11 17 5 4 5 0.071177 100/100 NonOverlappingTemplate + 17 11 9 11 15 4 9 11 7 6 0.122325 99/100 NonOverlappingTemplate + 7 10 9 6 7 17 10 14 11 9 0.334538 99/100 NonOverlappingTemplate + 10 6 7 11 9 13 7 14 11 12 0.678686 100/100 NonOverlappingTemplate + 6 12 10 9 10 5 11 12 12 13 0.699313 100/100 NonOverlappingTemplate + 8 8 11 15 10 8 12 11 11 6 0.739918 100/100 NonOverlappingTemplate + 16 7 10 12 11 11 11 6 8 8 0.574903 97/100 NonOverlappingTemplate + 12 7 12 8 12 11 6 14 6 12 0.554420 100/100 NonOverlappingTemplate + 19 8 8 13 11 11 8 10 7 5 0.129620 98/100 NonOverlappingTemplate + 16 13 12 8 8 10 11 5 14 3 0.096578 97/100 NonOverlappingTemplate + 8 14 9 8 12 6 11 8 8 16 0.437274 100/100 NonOverlappingTemplate + 13 12 7 7 7 10 7 14 9 14 0.514124 99/100 NonOverlappingTemplate + 9 6 6 7 13 10 14 5 15 15 0.115387 100/100 NonOverlappingTemplate + 6 12 12 13 7 11 13 8 10 8 0.739918 99/100 NonOverlappingTemplate + 11 16 12 5 12 10 12 8 11 3 0.171867 99/100 NonOverlappingTemplate + 4 10 10 11 10 6 11 13 10 15 0.455937 98/100 NonOverlappingTemplate + 13 4 13 10 11 13 11 9 6 10 0.514124 98/100 NonOverlappingTemplate + 8 8 10 9 11 12 12 13 14 3 0.419021 99/100 NonOverlappingTemplate + 10 13 7 9 11 11 11 8 7 13 0.883171 100/100 NonOverlappingTemplate + 10 3 9 15 10 15 10 6 13 9 0.181557 99/100 NonOverlappingTemplate + 9 11 13 4 15 6 8 9 13 12 0.304126 99/100 NonOverlappingTemplate + 9 11 13 7 12 9 8 7 15 9 0.699313 100/100 NonOverlappingTemplate + 14 6 13 9 14 8 11 8 4 13 0.262249 99/100 NonOverlappingTemplate + 8 15 7 12 8 12 10 8 8 12 0.719747 100/100 NonOverlappingTemplate + 9 9 6 10 12 14 15 8 10 7 0.574903 98/100 NonOverlappingTemplate + 12 13 9 12 13 8 8 9 9 7 0.867692 100/100 NonOverlappingTemplate + 14 9 8 7 13 13 10 11 6 9 0.678686 100/100 NonOverlappingTemplate + 5 10 13 10 7 13 8 11 9 14 0.595549 98/100 NonOverlappingTemplate + 7 5 15 14 10 8 12 8 9 12 0.419021 100/100 NonOverlappingTemplate + 10 14 8 9 14 5 8 9 12 11 0.616305 97/100 NonOverlappingTemplate + 9 19 12 8 9 10 5 10 5 13 0.090936 99/100 NonOverlappingTemplate + 8 14 10 8 10 11 9 9 17 4 0.262249 99/100 NonOverlappingTemplate + 12 11 10 9 12 7 11 7 13 8 0.897763 98/100 NonOverlappingTemplate + 11 15 11 12 10 8 9 10 5 9 0.719747 99/100 NonOverlappingTemplate + 11 16 12 7 10 9 13 13 6 3 0.145326 100/100 NonOverlappingTemplate + 14 14 6 7 12 10 14 7 8 8 0.401199 99/100 NonOverlappingTemplate + 11 7 14 4 9 9 9 11 12 14 0.474986 99/100 NonOverlappingTemplate + 8 8 12 15 14 7 7 11 9 9 0.595549 99/100 NonOverlappingTemplate + 10 13 10 10 10 7 5 14 10 11 0.739918 99/100 NonOverlappingTemplate + 10 6 8 10 14 11 9 9 10 13 0.851383 100/100 NonOverlappingTemplate + 12 7 15 11 9 15 9 8 5 9 0.383827 99/100 NonOverlappingTemplate + 9 10 9 9 10 11 14 13 7 8 0.897763 98/100 NonOverlappingTemplate + 8 9 15 12 15 8 12 9 9 3 0.224821 100/100 NonOverlappingTemplate + 11 9 9 14 14 12 6 5 11 9 0.514124 100/100 NonOverlappingTemplate + 10 15 7 12 12 3 12 13 9 7 0.249284 98/100 NonOverlappingTemplate + 7 9 7 12 9 7 7 13 15 14 0.419021 100/100 NonOverlappingTemplate + 13 10 11 8 13 7 2 11 14 11 0.249284 100/100 NonOverlappingTemplate + 9 18 8 11 10 15 7 9 8 5 0.145326 97/100 NonOverlappingTemplate + 8 12 11 8 16 12 6 8 7 12 0.474986 100/100 NonOverlappingTemplate + 11 11 10 14 8 16 5 13 6 6 0.191687 99/100 NonOverlappingTemplate + 11 8 11 10 10 10 7 9 13 11 0.978072 99/100 NonOverlappingTemplate + 5 12 14 8 7 10 13 13 9 9 0.554420 100/100 NonOverlappingTemplate + 11 11 10 7 12 6 11 8 10 14 0.816537 99/100 NonOverlappingTemplate + 12 9 7 8 7 14 10 12 10 11 0.851383 99/100 NonOverlappingTemplate + 8 12 8 12 9 10 10 9 14 8 0.924076 99/100 NonOverlappingTemplate + 13 11 3 4 7 12 15 12 16 7 0.032923 100/100 NonOverlappingTemplate + 12 15 8 5 10 13 13 7 8 9 0.437274 100/100 NonOverlappingTemplate + 9 7 6 9 10 13 14 7 14 11 0.554420 99/100 NonOverlappingTemplate + 8 9 8 8 16 10 9 11 10 11 0.816537 98/100 NonOverlappingTemplate + 13 7 8 3 14 12 15 5 13 10 0.090936 99/100 NonOverlappingTemplate + 8 6 4 12 9 11 8 15 11 16 0.171867 100/100 NonOverlappingTemplate + 10 8 9 14 9 10 8 9 9 14 0.883171 100/100 NonOverlappingTemplate + 17 9 13 8 8 11 6 11 8 9 0.437274 99/100 OverlappingTemplate + 14 7 9 3 11 14 15 7 11 9 0.171867 99/100 Universal + 7 11 14 6 9 10 14 7 10 12 0.616305 100/100 ApproximateEntropy + 7 6 2 10 5 8 5 6 2 6 0.224821 55/57 RandomExcursions + 9 5 6 4 8 6 2 7 4 6 0.474986 55/57 RandomExcursions + 6 4 4 11 8 10 4 4 2 4 0.048716 56/57 RandomExcursions + 8 9 5 8 1 7 4 2 8 5 0.102526 55/57 RandomExcursions + 12 2 6 10 2 3 5 4 8 5 0.010988 57/57 RandomExcursions + 9 8 5 7 4 7 2 6 4 5 0.437274 57/57 RandomExcursions + 9 5 8 4 4 7 6 2 5 7 0.437274 55/57 RandomExcursions + 11 7 7 4 4 3 7 6 3 5 0.224821 57/57 RandomExcursions + 8 7 6 6 9 4 4 5 2 6 0.474986 56/57 RandomExcursionsVariant + 8 8 8 4 7 4 6 4 2 6 0.437274 57/57 RandomExcursionsVariant + 6 11 2 9 10 4 0 4 4 7 0.004629 56/57 RandomExcursionsVariant + 6 7 10 9 9 0 8 2 2 4 0.006196 56/57 RandomExcursionsVariant + 8 5 8 12 7 3 7 1 3 3 0.014550 56/57 RandomExcursionsVariant + 8 4 11 5 7 7 4 2 4 5 0.162606 55/57 RandomExcursionsVariant + 5 6 5 3 8 5 8 6 6 5 0.834308 57/57 RandomExcursionsVariant + 8 5 4 10 5 1 5 4 7 8 0.162606 57/57 RandomExcursionsVariant + 12 4 6 4 5 4 6 6 6 4 0.249284 55/57 RandomExcursionsVariant + 8 5 6 5 3 9 3 7 3 8 0.334538 57/57 RandomExcursionsVariant + 6 9 3 6 6 8 2 8 3 6 0.275709 56/57 RandomExcursionsVariant + 6 8 6 5 5 6 4 3 7 7 0.834308 57/57 RandomExcursionsVariant + 7 4 2 9 9 4 7 3 7 5 0.224821 57/57 RandomExcursionsVariant + 6 7 8 8 5 5 3 2 6 7 0.514124 57/57 RandomExcursionsVariant + 5 15 5 4 5 4 2 5 4 8 0.003996 57/57 RandomExcursionsVariant + 7 12 9 1 3 3 3 8 5 6 0.010988 57/57 RandomExcursionsVariant + 7 5 7 8 4 6 2 6 6 6 0.719747 57/57 RandomExcursionsVariant + 7 3 6 14 3 2 3 3 8 8 0.002203 57/57 RandomExcursionsVariant + 6 8 12 9 19 9 10 6 9 12 0.171867 100/100 Serial + 7 11 11 15 10 9 11 5 10 11 0.699313 100/100 Serial + 9 19 9 10 10 12 12 5 6 8 0.137282 98/100 LinearComplexity + + +- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - +The minimum pass rate for each statistical test with the exception of the +random excursion (variant) test is approximately = 96 for a +sample size = 100 binary sequences. + +The minimum pass rate for the random excursion (variant) test +is approximately = 54 for a sample size = 57 binary sequences. + +For further guidelines construct a probability table using the MAPLE program +provided in the addendum section of the documentation. +- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - diff --git a/experiments/qian/finalAnalysisReport_jf_oldci_stable_b_6bit.txt b/experiments/qian/finalAnalysisReport_jf_oldci_stable_b_6bit.txt new file mode 100644 index 0000000..9354d9f --- /dev/null +++ b/experiments/qian/finalAnalysisReport_jf_oldci_stable_b_6bit.txt @@ -0,0 +1,208 @@ +------------------------------------------------------------------------------ +RESULTS FOR THE UNIFORMITY OF P-VALUES AND THE PROPORTION OF PASSING SEQUENCES +------------------------------------------------------------------------------ + generator is +------------------------------------------------------------------------------ + C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 P-VALUE PROPORTION STATISTICAL TEST +------------------------------------------------------------------------------ + 9 10 5 6 10 14 13 10 13 10 0.574903 99/100 Frequency + 11 12 7 13 11 9 9 6 13 9 0.816537 98/100 BlockFrequency + 8 7 10 13 6 8 12 9 12 15 0.574903 99/100 CumulativeSums + 8 4 13 6 12 16 11 6 12 12 0.162606 99/100 CumulativeSums + 11 5 14 11 8 10 14 10 9 8 0.657933 98/100 Runs + 14 9 9 12 8 5 12 10 14 7 0.534146 100/100 LongestRun + 10 12 12 8 9 14 6 9 6 14 0.554420 99/100 Rank + 14 15 10 6 12 9 9 11 4 10 0.350485 98/100 FFT + 9 15 14 7 6 10 10 6 8 15 0.262249 98/100 NonOverlappingTemplate + 6 14 10 10 7 9 7 12 9 16 0.419021 100/100 NonOverlappingTemplate + 5 11 14 8 12 8 8 9 17 8 0.262249 100/100 NonOverlappingTemplate + 9 7 10 8 18 8 12 9 11 8 0.419021 100/100 NonOverlappingTemplate + 9 7 7 14 13 9 9 8 8 16 0.437274 100/100 NonOverlappingTemplate + 8 15 5 11 12 14 7 4 8 16 0.066882 98/100 NonOverlappingTemplate + 11 8 13 11 10 13 10 13 9 2 0.366918 100/100 NonOverlappingTemplate + 14 16 15 8 4 14 4 10 9 6 0.028817 98/100 NonOverlappingTemplate + 11 8 11 13 5 12 9 12 11 8 0.798139 98/100 NonOverlappingTemplate + 14 9 11 15 5 5 10 10 9 12 0.366918 99/100 NonOverlappingTemplate + 12 9 7 12 15 10 6 11 9 9 0.719747 100/100 NonOverlappingTemplate + 10 11 6 13 6 10 14 9 12 9 0.699313 99/100 NonOverlappingTemplate + 11 8 11 7 14 9 15 9 9 7 0.657933 98/100 NonOverlappingTemplate + 9 5 16 11 10 11 7 8 13 10 0.474986 99/100 NonOverlappingTemplate + 7 11 9 13 8 13 21 10 4 4 0.007160 99/100 NonOverlappingTemplate + 16 11 14 11 6 11 9 8 7 7 0.401199 97/100 NonOverlappingTemplate + 12 16 12 11 10 6 8 8 10 7 0.554420 99/100 NonOverlappingTemplate + 11 10 12 12 12 7 5 10 14 7 0.616305 100/100 NonOverlappingTemplate + 13 10 15 9 11 10 12 6 8 6 0.574903 99/100 NonOverlappingTemplate + 9 9 8 9 13 12 12 9 9 10 0.978072 99/100 NonOverlappingTemplate + 14 6 8 9 15 5 10 20 3 10 0.004981 99/100 NonOverlappingTemplate + 8 6 13 10 7 12 13 12 7 12 0.657933 100/100 NonOverlappingTemplate + 9 9 10 9 9 10 10 10 16 8 0.883171 100/100 NonOverlappingTemplate + 6 17 9 11 13 7 15 12 4 6 0.055361 98/100 NonOverlappingTemplate + 5 9 15 7 16 8 8 10 12 10 0.289667 100/100 NonOverlappingTemplate + 7 7 12 12 9 7 8 14 15 9 0.514124 99/100 NonOverlappingTemplate + 8 11 5 9 13 11 12 12 9 10 0.834308 99/100 NonOverlappingTemplate + 9 6 12 12 16 6 11 8 9 11 0.494392 100/100 NonOverlappingTemplate + 8 9 7 6 10 9 18 12 10 11 0.350485 100/100 NonOverlappingTemplate + 7 12 4 14 16 11 14 8 5 9 0.096578 99/100 NonOverlappingTemplate + 11 11 9 13 12 7 14 8 7 8 0.759756 100/100 NonOverlappingTemplate + 10 11 4 9 12 8 12 12 9 13 0.699313 100/100 NonOverlappingTemplate + 15 15 8 9 11 15 5 7 4 11 0.085587 97/100 NonOverlappingTemplate + 12 9 10 10 14 9 9 8 10 9 0.971699 99/100 NonOverlappingTemplate + 6 14 6 13 8 9 10 14 10 10 0.554420 100/100 NonOverlappingTemplate + 13 11 4 6 11 12 13 14 9 7 0.334538 98/100 NonOverlappingTemplate + 7 9 9 11 8 11 10 8 14 13 0.867692 99/100 NonOverlappingTemplate + 18 14 12 5 14 8 13 7 5 4 0.013569 100/100 NonOverlappingTemplate + 9 16 7 8 7 7 17 5 14 10 0.071177 100/100 NonOverlappingTemplate + 7 9 13 7 7 10 16 12 8 11 0.514124 99/100 NonOverlappingTemplate + 16 5 9 9 8 8 6 11 12 16 0.171867 99/100 NonOverlappingTemplate + 7 11 8 8 11 11 7 14 6 17 0.275709 99/100 NonOverlappingTemplate + 12 11 7 9 8 13 11 5 9 15 0.534146 99/100 NonOverlappingTemplate + 7 6 6 16 14 13 5 10 12 11 0.153763 98/100 NonOverlappingTemplate + 11 7 6 8 11 9 14 12 10 12 0.779188 100/100 NonOverlappingTemplate + 9 13 10 12 8 9 9 8 15 7 0.759756 99/100 NonOverlappingTemplate + 14 8 12 12 11 5 7 4 12 15 0.171867 99/100 NonOverlappingTemplate + 10 10 17 8 5 10 12 15 8 5 0.137282 98/100 NonOverlappingTemplate + 10 11 13 9 18 7 10 10 9 3 0.145326 99/100 NonOverlappingTemplate + 10 9 17 13 8 5 9 13 8 8 0.304126 100/100 NonOverlappingTemplate + 5 11 11 8 10 11 11 16 10 7 0.554420 98/100 NonOverlappingTemplate + 8 11 15 10 8 9 12 9 7 11 0.834308 100/100 NonOverlappingTemplate + 10 17 11 11 9 7 9 10 10 6 0.554420 99/100 NonOverlappingTemplate + 12 10 11 7 10 10 3 14 11 12 0.494392 100/100 NonOverlappingTemplate + 10 4 3 9 13 10 12 18 12 9 0.051942 100/100 NonOverlappingTemplate + 13 10 10 10 10 3 9 10 8 17 0.262249 100/100 NonOverlappingTemplate + 10 9 16 10 10 9 5 5 18 8 0.075719 100/100 NonOverlappingTemplate + 11 11 9 8 11 12 13 10 6 9 0.924076 100/100 NonOverlappingTemplate + 10 12 8 11 11 6 14 8 9 11 0.851383 100/100 NonOverlappingTemplate + 11 12 10 14 12 6 11 8 9 7 0.779188 100/100 NonOverlappingTemplate + 11 9 12 8 8 14 12 4 11 11 0.616305 98/100 NonOverlappingTemplate + 10 11 6 6 11 6 14 15 11 10 0.419021 99/100 NonOverlappingTemplate + 13 13 12 9 8 12 8 7 11 7 0.798139 98/100 NonOverlappingTemplate + 8 14 10 7 7 8 13 13 12 8 0.657933 99/100 NonOverlappingTemplate + 10 8 6 12 11 11 11 10 11 10 0.971699 99/100 NonOverlappingTemplate + 12 11 14 11 8 9 14 10 5 6 0.494392 100/100 NonOverlappingTemplate + 7 12 15 4 13 10 13 6 11 9 0.275709 100/100 NonOverlappingTemplate + 11 10 8 7 8 8 13 10 9 16 0.657933 99/100 NonOverlappingTemplate + 11 7 11 4 15 8 9 10 15 10 0.334538 98/100 NonOverlappingTemplate + 11 10 10 8 10 8 8 17 9 9 0.699313 98/100 NonOverlappingTemplate + 8 3 13 12 3 9 11 16 18 7 0.007160 96/100 NonOverlappingTemplate + 19 10 10 9 10 7 8 14 8 5 0.122325 99/100 NonOverlappingTemplate + 7 12 11 14 7 9 9 14 6 11 0.595549 99/100 NonOverlappingTemplate + 7 7 7 9 6 17 15 5 10 17 0.023545 98/100 NonOverlappingTemplate + 9 15 14 7 6 10 10 6 8 15 0.262249 98/100 NonOverlappingTemplate + 14 9 8 7 17 6 9 10 7 13 0.249284 99/100 NonOverlappingTemplate + 9 9 7 16 9 12 17 7 7 7 0.171867 100/100 NonOverlappingTemplate + 10 11 5 7 9 12 13 10 12 11 0.798139 100/100 NonOverlappingTemplate + 8 14 12 13 7 9 11 7 12 7 0.678686 100/100 NonOverlappingTemplate + 13 11 8 9 11 9 11 8 10 10 0.987896 99/100 NonOverlappingTemplate + 6 7 9 8 12 14 13 12 7 12 0.574903 99/100 NonOverlappingTemplate + 8 8 11 11 11 9 13 10 11 8 0.978072 100/100 NonOverlappingTemplate + 8 13 11 14 5 9 9 13 7 11 0.574903 100/100 NonOverlappingTemplate + 7 6 10 11 12 10 8 7 16 13 0.455937 100/100 NonOverlappingTemplate + 5 9 3 9 8 10 10 10 13 23 0.002203 99/100 NonOverlappingTemplate + 6 6 10 9 9 10 15 7 13 15 0.334538 99/100 NonOverlappingTemplate + 10 9 11 7 10 6 11 8 10 18 0.383827 100/100 NonOverlappingTemplate + 9 11 5 6 12 18 11 9 6 13 0.129620 99/100 NonOverlappingTemplate + 12 9 6 12 11 14 11 10 12 3 0.383827 100/100 NonOverlappingTemplate + 10 14 11 9 8 9 7 15 9 8 0.719747 99/100 NonOverlappingTemplate + 10 6 10 10 9 7 15 8 6 19 0.085587 98/100 NonOverlappingTemplate + 13 11 9 9 10 7 14 5 9 13 0.616305 98/100 NonOverlappingTemplate + 4 8 9 10 14 14 7 13 12 9 0.383827 100/100 NonOverlappingTemplate + 16 15 6 9 10 9 13 9 7 6 0.249284 100/100 NonOverlappingTemplate + 11 5 10 4 11 13 17 9 13 7 0.122325 100/100 NonOverlappingTemplate + 6 17 12 11 9 9 13 6 13 4 0.115387 100/100 NonOverlappingTemplate + 15 5 6 19 10 10 9 10 5 11 0.042808 99/100 NonOverlappingTemplate + 14 10 7 11 7 5 12 11 14 9 0.514124 99/100 NonOverlappingTemplate + 10 7 11 9 12 5 10 7 12 17 0.334538 100/100 NonOverlappingTemplate + 9 15 5 4 7 8 10 12 16 14 0.075719 98/100 NonOverlappingTemplate + 7 13 10 14 9 8 14 11 9 5 0.514124 99/100 NonOverlappingTemplate + 9 13 10 7 4 10 18 9 8 12 0.171867 98/100 NonOverlappingTemplate + 10 7 9 9 7 13 13 9 12 11 0.883171 98/100 NonOverlappingTemplate + 7 13 12 7 13 7 10 5 14 12 0.401199 99/100 NonOverlappingTemplate + 9 10 12 16 10 6 11 5 12 9 0.455937 100/100 NonOverlappingTemplate + 9 9 12 10 13 11 6 11 10 9 0.946308 99/100 NonOverlappingTemplate + 5 16 8 9 11 5 10 15 6 15 0.071177 100/100 NonOverlappingTemplate + 12 16 11 9 7 8 10 8 11 8 0.699313 98/100 NonOverlappingTemplate + 15 12 8 13 2 9 12 12 7 10 0.191687 96/100 NonOverlappingTemplate + 9 10 10 7 9 11 11 8 6 19 0.249284 99/100 NonOverlappingTemplate + 8 10 8 11 13 9 14 9 7 11 0.867692 100/100 NonOverlappingTemplate + 7 3 7 10 13 14 14 16 6 10 0.066882 99/100 NonOverlappingTemplate + 12 9 9 10 7 12 16 6 10 9 0.616305 99/100 NonOverlappingTemplate + 10 13 11 10 8 7 12 10 6 13 0.816537 100/100 NonOverlappingTemplate + 9 12 6 11 9 5 18 11 4 15 0.042808 100/100 NonOverlappingTemplate + 20 13 7 10 8 4 11 10 9 8 0.058984 98/100 NonOverlappingTemplate + 13 12 15 12 9 5 8 9 10 7 0.514124 96/100 NonOverlappingTemplate + 8 16 10 11 11 8 7 7 7 15 0.366918 99/100 NonOverlappingTemplate + 4 9 7 7 16 13 9 6 13 16 0.062821 99/100 NonOverlappingTemplate + 11 13 8 7 4 15 9 14 10 9 0.334538 97/100 NonOverlappingTemplate + 10 13 8 11 13 7 11 9 11 7 0.883171 100/100 NonOverlappingTemplate + 8 13 13 12 9 8 10 6 14 7 0.616305 100/100 NonOverlappingTemplate + 3 12 7 9 9 14 10 9 14 13 0.304126 100/100 NonOverlappingTemplate + 9 10 9 9 10 9 17 9 9 9 0.779188 100/100 NonOverlappingTemplate + 7 12 12 7 7 10 14 10 12 9 0.779188 99/100 NonOverlappingTemplate + 4 7 15 13 10 11 8 15 12 5 0.129620 100/100 NonOverlappingTemplate + 8 6 11 9 10 16 14 9 5 12 0.319084 100/100 NonOverlappingTemplate + 11 9 9 8 12 9 12 11 13 6 0.897763 98/100 NonOverlappingTemplate + 14 12 8 7 10 11 10 11 6 11 0.816537 96/100 NonOverlappingTemplate + 13 7 13 8 9 15 9 4 8 14 0.249284 97/100 NonOverlappingTemplate + 5 6 10 12 8 9 13 9 15 13 0.401199 98/100 NonOverlappingTemplate + 13 14 13 8 10 6 12 10 9 5 0.494392 99/100 NonOverlappingTemplate + 9 11 12 14 11 4 13 6 6 14 0.236810 100/100 NonOverlappingTemplate + 7 8 8 11 13 12 10 9 14 8 0.816537 99/100 NonOverlappingTemplate + 7 9 13 5 10 18 8 11 6 13 0.129620 99/100 NonOverlappingTemplate + 9 9 7 12 11 9 13 9 15 6 0.657933 96/100 NonOverlappingTemplate + 6 14 13 8 14 8 12 7 12 6 0.366918 99/100 NonOverlappingTemplate + 6 12 8 16 9 7 11 9 11 11 0.595549 100/100 NonOverlappingTemplate + 8 6 17 12 5 10 10 8 7 17 0.066882 99/100 NonOverlappingTemplate + 15 8 12 7 8 14 12 9 6 9 0.494392 97/100 NonOverlappingTemplate + 10 12 7 14 10 11 4 10 10 12 0.637119 99/100 NonOverlappingTemplate + 13 4 7 7 11 7 11 9 15 16 0.137282 99/100 NonOverlappingTemplate + 6 7 6 11 16 12 12 6 12 12 0.275709 100/100 NonOverlappingTemplate + 6 9 10 5 9 10 14 10 12 15 0.455937 100/100 NonOverlappingTemplate + 7 7 9 13 10 14 7 12 8 13 0.637119 98/100 NonOverlappingTemplate + 8 16 11 7 12 7 7 10 9 13 0.514124 98/100 NonOverlappingTemplate + 6 9 14 6 13 10 10 11 12 9 0.699313 100/100 NonOverlappingTemplate + 7 7 7 9 6 17 15 5 10 17 0.023545 98/100 NonOverlappingTemplate + 11 11 8 8 8 14 11 6 9 14 0.699313 100/100 OverlappingTemplate + 13 22 6 15 6 3 5 11 12 7 0.000474 97/100 Universal + 11 15 6 10 11 13 13 7 9 5 0.383827 99/100 ApproximateEntropy + 6 6 6 7 8 3 4 6 8 7 0.922036 60/61 RandomExcursions + 6 5 8 6 7 7 5 3 6 8 0.941144 60/61 RandomExcursions + 5 4 12 6 5 1 10 6 8 4 0.086458 60/61 RandomExcursions + 4 8 5 10 3 9 5 8 7 2 0.287306 61/61 RandomExcursions + 5 4 9 6 8 9 4 7 6 3 0.654467 61/61 RandomExcursions + 3 4 3 14 6 6 7 4 6 8 0.070445 61/61 RandomExcursions + 3 5 7 12 7 3 3 5 9 7 0.170294 60/61 RandomExcursions + 2 4 11 4 4 7 9 7 8 5 0.242986 61/61 RandomExcursions + 10 4 6 12 4 4 7 2 4 8 0.095617 61/61 RandomExcursionsVariant + 7 7 7 11 5 4 4 7 5 4 0.619772 61/61 RandomExcursionsVariant + 7 9 7 7 6 5 7 2 2 9 0.422034 60/61 RandomExcursionsVariant + 8 6 7 10 5 6 2 4 8 5 0.551026 61/61 RandomExcursionsVariant + 8 8 7 7 7 6 3 8 3 4 0.723129 59/61 RandomExcursionsVariant + 8 12 3 7 7 5 7 3 3 6 0.222869 61/61 RandomExcursionsVariant + 7 8 8 6 5 9 2 5 6 5 0.723129 61/61 RandomExcursionsVariant + 5 7 7 8 8 4 5 5 7 5 0.957319 60/61 RandomExcursionsVariant + 6 9 8 3 5 3 8 7 5 7 0.689019 60/61 RandomExcursionsVariant + 5 13 6 9 6 3 6 3 3 7 0.105618 61/61 RandomExcursionsVariant + 7 7 7 11 6 6 4 3 6 4 0.585209 60/61 RandomExcursionsVariant + 5 5 10 5 9 6 6 6 6 3 0.723129 60/61 RandomExcursionsVariant + 5 5 9 5 6 4 2 6 10 9 0.392456 60/61 RandomExcursionsVariant + 3 9 6 6 4 9 7 5 2 10 0.287306 60/61 RandomExcursionsVariant + 4 8 5 5 16 7 2 4 3 7 0.005166 60/61 RandomExcursionsVariant + 4 3 10 10 9 4 6 7 6 2 0.186566 61/61 RandomExcursionsVariant + 3 7 7 11 9 7 3 5 4 5 0.337162 61/61 RandomExcursionsVariant + 4 7 5 11 8 8 3 5 5 5 0.484646 61/61 RandomExcursionsVariant + 7 11 11 8 16 8 12 11 7 9 0.637119 99/100 Serial + 14 10 7 6 9 14 10 11 6 13 0.494392 97/100 Serial + 8 10 9 15 12 9 11 9 7 10 0.867692 99/100 LinearComplexity + + +- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - +The minimum pass rate for each statistical test with the exception of the +random excursion (variant) test is approximately = 96 for a +sample size = 100 binary sequences. + +The minimum pass rate for the random excursion (variant) test +is approximately = 58 for a sample size = 61 binary sequences. + +For further guidelines construct a probability table using the MAPLE program +provided in the addendum section of the documentation. +- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - diff --git a/experiments/qian/finalAnalysisReport_jf_oldci_stable_b_8bit.txt b/experiments/qian/finalAnalysisReport_jf_oldci_stable_b_8bit.txt new file mode 100644 index 0000000..8434b5b --- /dev/null +++ b/experiments/qian/finalAnalysisReport_jf_oldci_stable_b_8bit.txt @@ -0,0 +1,208 @@ +------------------------------------------------------------------------------ +RESULTS FOR THE UNIFORMITY OF P-VALUES AND THE PROPORTION OF PASSING SEQUENCES +------------------------------------------------------------------------------ + generator is +------------------------------------------------------------------------------ + C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 P-VALUE PROPORTION STATISTICAL TEST +------------------------------------------------------------------------------ + 16 10 10 11 11 11 6 8 9 8 0.699313 96/100 Frequency + 10 14 8 5 9 11 7 14 14 8 0.419021 99/100 BlockFrequency + 15 10 12 14 9 7 10 4 9 10 0.419021 97/100 CumulativeSums + 14 9 9 10 12 11 5 9 8 13 0.719747 97/100 CumulativeSums + 11 10 8 9 11 8 5 14 15 9 0.554420 99/100 Runs + 11 6 11 7 12 9 16 12 8 8 0.534146 98/100 LongestRun + 8 10 12 11 14 9 7 8 11 10 0.911413 99/100 Rank + 7 13 19 7 10 6 7 8 14 9 0.080519 99/100 FFT + 10 10 4 12 11 5 15 9 9 15 0.224821 99/100 NonOverlappingTemplate + 7 14 11 6 9 8 8 6 22 9 0.011791 100/100 NonOverlappingTemplate + 9 7 12 11 7 12 8 10 9 15 0.759756 100/100 NonOverlappingTemplate + 12 9 13 9 9 12 7 12 7 10 0.897763 99/100 NonOverlappingTemplate + 8 8 11 12 10 9 8 6 13 15 0.657933 100/100 NonOverlappingTemplate + 5 11 11 18 12 9 12 6 10 6 0.153763 99/100 NonOverlappingTemplate + 8 13 15 11 8 4 11 9 9 12 0.474986 99/100 NonOverlappingTemplate + 16 8 9 12 8 7 14 6 12 8 0.366918 98/100 NonOverlappingTemplate + 7 6 8 11 12 10 9 12 15 10 0.699313 99/100 NonOverlappingTemplate + 9 16 10 5 10 10 10 15 7 8 0.350485 99/100 NonOverlappingTemplate + 11 7 6 14 10 6 16 20 3 7 0.002758 100/100 NonOverlappingTemplate + 9 9 11 14 7 9 8 8 10 15 0.719747 100/100 NonOverlappingTemplate + 14 10 9 10 8 9 10 17 7 6 0.383827 100/100 NonOverlappingTemplate + 5 13 10 12 16 8 11 7 7 11 0.366918 100/100 NonOverlappingTemplate + 12 12 8 8 13 13 7 13 9 5 0.554420 98/100 NonOverlappingTemplate + 15 9 8 11 5 10 11 11 9 11 0.739918 98/100 NonOverlappingTemplate + 8 7 9 14 8 9 9 6 14 16 0.319084 100/100 NonOverlappingTemplate + 13 5 9 10 9 20 8 8 10 8 0.096578 99/100 NonOverlappingTemplate + 9 8 12 12 6 14 8 10 12 9 0.798139 98/100 NonOverlappingTemplate + 14 6 8 7 12 6 14 12 8 13 0.366918 97/100 NonOverlappingTemplate + 12 6 13 9 8 14 9 8 9 12 0.739918 99/100 NonOverlappingTemplate + 10 6 11 11 6 9 9 12 16 10 0.574903 99/100 NonOverlappingTemplate + 8 14 5 11 13 10 6 13 13 7 0.366918 98/100 NonOverlappingTemplate + 13 13 9 8 9 12 10 6 8 12 0.816537 97/100 NonOverlappingTemplate + 10 11 9 8 8 12 9 13 11 9 0.978072 99/100 NonOverlappingTemplate + 7 9 13 11 10 14 8 12 7 9 0.798139 99/100 NonOverlappingTemplate + 10 8 10 11 10 6 13 8 13 11 0.883171 99/100 NonOverlappingTemplate + 13 10 7 10 14 8 5 12 14 7 0.419021 99/100 NonOverlappingTemplate + 16 15 14 6 9 9 5 5 11 10 0.102526 99/100 NonOverlappingTemplate + 6 9 5 10 7 11 16 14 11 11 0.304126 100/100 NonOverlappingTemplate + 9 10 6 12 13 14 8 11 7 10 0.739918 99/100 NonOverlappingTemplate + 9 14 8 13 11 6 11 10 11 7 0.759756 99/100 NonOverlappingTemplate + 14 4 11 11 7 6 13 13 11 10 0.366918 97/100 NonOverlappingTemplate + 14 12 6 12 10 14 3 9 11 9 0.289667 98/100 NonOverlappingTemplate + 15 13 13 10 9 3 11 10 5 11 0.213309 99/100 NonOverlappingTemplate + 8 7 10 12 13 11 9 9 10 11 0.964295 100/100 NonOverlappingTemplate + 11 10 15 13 5 12 6 6 9 13 0.304126 99/100 NonOverlappingTemplate + 7 13 5 10 6 13 15 11 9 11 0.383827 99/100 NonOverlappingTemplate + 4 10 10 11 14 11 11 8 9 12 0.699313 99/100 NonOverlappingTemplate + 7 11 6 10 13 5 15 14 10 9 0.334538 100/100 NonOverlappingTemplate + 12 7 11 13 9 10 12 5 10 11 0.798139 98/100 NonOverlappingTemplate + 11 4 10 18 10 5 13 12 11 6 0.075719 99/100 NonOverlappingTemplate + 10 10 8 6 7 15 6 15 11 12 0.350485 99/100 NonOverlappingTemplate + 10 13 6 10 13 10 11 8 8 11 0.883171 100/100 NonOverlappingTemplate + 13 11 9 12 9 8 8 12 6 12 0.851383 100/100 NonOverlappingTemplate + 10 11 5 8 11 13 8 10 11 13 0.798139 99/100 NonOverlappingTemplate + 10 5 10 10 14 12 11 14 10 4 0.366918 99/100 NonOverlappingTemplate + 5 11 11 10 12 13 18 3 12 5 0.032923 100/100 NonOverlappingTemplate + 9 10 16 7 8 12 13 5 9 11 0.437274 100/100 NonOverlappingTemplate + 12 10 8 11 8 12 12 9 9 9 0.983453 99/100 NonOverlappingTemplate + 9 13 12 8 10 6 10 9 11 12 0.911413 100/100 NonOverlappingTemplate + 10 11 7 11 17 12 7 6 9 10 0.437274 99/100 NonOverlappingTemplate + 9 8 13 9 13 11 11 7 11 8 0.911413 99/100 NonOverlappingTemplate + 9 12 12 14 10 7 9 8 10 9 0.911413 99/100 NonOverlappingTemplate + 6 12 16 12 9 10 7 12 8 8 0.514124 100/100 NonOverlappingTemplate + 13 15 9 10 12 15 5 8 9 4 0.162606 99/100 NonOverlappingTemplate + 3 9 11 10 20 5 6 12 14 10 0.011791 100/100 NonOverlappingTemplate + 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+ +- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - +The minimum pass rate for each statistical test with the exception of the +random excursion (variant) test is approximately = 96 for a +sample size = 100 binary sequences. + +The minimum pass rate for the random excursion (variant) test +is approximately = 57 for a sample size = 60 binary sequences. + +For further guidelines construct a probability table using the MAPLE program +provided in the addendum section of the documentation. +- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - diff --git a/experiments/res2.txt b/experiments/res2.txt new file mode 100644 index 0000000..1c6a0fe --- /dev/null +++ b/experiments/res2.txt @@ -0,0 +1 @@ +[[0,1,1,0],[1,0,0,1],[1,0,0,1],[0,1,1,0]][[0,1,1,0],[1,0,0,1],[1,0,1,0],[0,1,0,1]][[0,1,1,0],[1,1,0,0],[1,0,0,1],[0,0,1,1]][[1,0,1,0],[0,1,0,1],[1,0,0,1],[0,1,1,0]][[1,0,1,0],[1,1,0,0],[0,0,1,1],[0,1,0,1]][[1,1,0,0],[0,1,0,1],[1,0,1,0],[0,0,1,1]][[1,1,0,0],[1,0,0,1],[0,0,1,1],[0,1,1,0]][[0,1,1,0],[1,0,0,1],[1,0,0,1],[0,1,1,0]][[0,1,1,0],[1,0,0,1],[1,0,1,0],[0,1,0,1]][[0,1,1,0],[1,1,0,0],[1,0,0,1],[0,0,1,1]][[1,0,1,0],[0,1,0,1],[1,0,0,1],[0,1,1,0]][[1,0,1,0],[1,1,0,0],[0,0,1,1],[0,1,0,1]][[1,1,0,0],[0,1,0,1],[1,0,1,0],[0,0,1,1]][[1,1,0,0],[1,0,0,1],[0,0,1,1],[0,1,1,0]][[0,1,1,0],[1,0,0,1],[1,0,0,1],[0,1,1,0]][[0,1,1,0],[1,0,0,1],[1,0,1,0],[0,1,0,1]][[0,1,1,0],[1,1,0,0],[1,0,0,1],[0,0,1,1]][[1,0,1,0],[0,1,0,1],[1,0,0,1],[0,1,1,0]][[1,0,1,0],[1,1,0,0],[0,0,1,1],[0,1,0,1]][[1,1,0,0],[0,1,0,1],[1,0,1,0],[0,0,1,1]][[1,1,0,0],[1,0,0,1],[0,0,1,1],[0,1,1,0]][[0,1,1,0],[1,0,0,1],[1,0,0,1],[0,1,1,0]][[0,1,1,0],[1,0,0,1],[1,0,1,0],[0,1,0,1]][[0,1,1,0],[1,1,0,0],[1,0,0,1],[0,0,1,1]][[1,0,1,0],[0,1,0,1],[1,0,0,1],[0,1,1,0]][[1,0,1,0],[1,1,0,0],[0,0,1,1],[0,1,0,1]][[1,1,0,0],[0,1,0,1],[1,0,1,0],[0,0,1,1]][[1,1,0,0],[1,0,0,1],[0,0,1,1],[0,1,1,0]][[0,1,1,0],[1,0,0,1],[1,0,0,1],[0,1,1,0]][[0,1,1,0],[1,0,0,1],[1,0,1,0],[0,1,0,1]][[0,1,1,0],[1,1,0,0],[1,0,0,1],[0,0,1,1]][[1,0,1,0],[0,1,0,1],[1,0,0,1],[0,1,1,0]][[1,0,1,0],[1,1,0,0],[0,0,1,1],[0,1,0,1]][[1,1,0,0],[0,1,0,1],[1,0,1,0],[0,0,1,1]][[1,1,0,0],[1,0,0,1],[0,0,1,1],[0,1,1,0]][[0,1,1,0],[1,0,0,1],[1,0,0,1],[0,1,1,0]][[0,1,1,0],[1,0,0,1],[1,0,1,0],[0,1,0,1]][[0,1,1,0],[1,1,0,0],[1,0,0,1],[0,0,1,1]][[1,0,1,0],[0,1,0,1],[1,0,0,1],[0,1,1,0]][[1,0,1,0],[1,1,0,0],[0,0,1,1],[0,1,0,1]][[1,1,0,0],[0,1,0,1],[1,0,1,0],[0,0,1,1]][[1,1,0,0],[1,0,0,1],[0,0,1,1],[0,1,1,0]][[0,1,1,0],[1,0,0,1],[1,0,0,1],[0,1,1,0]][[0,1,1,0],[1,0,0,1],[1,0,1,0],[0,1,0,1]][[0,1,1,0],[1,1,0,0],[1,0,0,1],[0,0,1,1]][[1,0,1,0],[0,1,0,1],[1,0,0,1],[0,1,1,0]][[1,0,1,0],[1,1,0,0],[0,0,1,1],[0,1,0,1]][[1,1,0,0],[0,1,0,1],[1,0,1,0],[0,0,1,1]][[1,1,0,0],[1,0,0,1],[0,0,1,1],[0,1,1,0]] 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4379 +ds calcul 1708 4379 +ds calcul 1709 4379 +ds calcul 1710 4384 +ds calcul 1711 4387 +ds calcul 1712 4387 +ds calcul 1713 4387 +ds calcul 1714 4390 +ds calcul 1715 4393 +ds calcul 1716 4393 +ds calcul 1717 4393 +ds calcul 1718 4393 +ds calcul 1719 4394 +ds calcul 1720 4394 +ds calcul 1721 4394 +ds calcul 1722 4397 +ds calcul 1723 4399 +ds calcul 1724 4400 +ds calcul 1725 4400 +ds calcul 1726 4400 +ds calcul 1727 4402 +ds calcul 1728 4404 +ds calcul 1729 4404 +ds calcul 1730 4404 +ds calcul 1731 4407 +ds calcul 1732 4409 +ds calcul 1733 4409 +ds calcul 1734 4409 +ds calcul 1735 4409 +ds calcul 1736 4411 +ds calcul 1737 4412 +ds calcul 1738 4413 +ds calcul 1739 4413 +ds calcul 1740 4413 +ds calcul 1741 4413 +ds calcul 1742 4413 +ds calcul 1743 4413 +ds calcul 1744 4417 +ds calcul 1745 4420 +ds calcul 1746 4423 +ds calcul 1747 4423 +ds calcul 1748 4423 +ds calcul 1749 4423 +ds calcul 1750 4427 +ds calcul 1751 4430 +ds calcul 1752 4433 +ds calcul 1753 4433 +ds calcul 1754 4433 +ds 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4465 +ds calcul 1803 4465 +ds calcul 1804 4465 +ds calcul 1805 4465 +ds calcul 1806 4465 +ds calcul 1807 4465 +ds calcul 1808 4465 +ds calcul 1809 4465 +ds calcul 1810 4465 +ds calcul 1811 4465 +ds calcul 1812 4465 +ds calcul 1813 4465 +ds calcul 1814 4465 +ds calcul 1815 4465 +ds calcul 1816 4465 +ds calcul 1817 4465 +ds calcul 1818 4465 +ds calcul 1819 4465 +ds calcul 1820 4465 +ds calcul 1821 4465 +ds calcul 1822 4465 +ds calcul 1823 4465 +ds calcul 1824 4465 +ds calcul 1825 4465 +ds calcul 1826 4465 +ds calcul 1827 4465 +ds calcul 1828 4465 +ds calcul 1829 4465 +ds calcul 1830 4466 +ds calcul 1831 4469 +ds calcul 1832 4472 +ds calcul 1833 4472 +ds calcul 1834 4472 +ds calcul 1835 4472 +ds calcul 1836 4474 +ds calcul 1837 4477 +ds calcul 1838 4477 +ds calcul 1839 4477 +ds calcul 1840 4477 +ds calcul 1841 4477 +ds calcul 1842 4477 +ds calcul 1843 4477 +ds calcul 1844 4477 +ds calcul 1845 4479 +ds calcul 1846 4482 +ds calcul 1847 4485 +ds calcul 1848 4485 +ds calcul 1849 4485 +ds calcul 1850 4485 +ds calcul 1851 4488 +ds calcul 1852 4491 +ds calcul 1853 4494 +ds calcul 1854 4494 +ds calcul 1855 4494 +ds calcul 1856 4494 +ds calcul 1857 4497 +ds calcul 1858 4500 +ds calcul 1859 4500 +ds calcul 1860 4500 +ds calcul 1861 4500 +ds calcul 1862 4500 +ds calcul 1863 4500 +ds calcul 1864 4500 +ds calcul 1865 4500 +ds calcul 1866 4500 +ds calcul 1867 4500 +ds calcul 1868 4500 +ds calcul 1869 4500 +ds calcul 1870 4500 +ds calcul 1871 4500 +ds calcul 1872 4500 +ds calcul 1873 4500 +ds calcul 1874 4500 +ds calcul 1875 4500 +ds calcul 1876 4500 +ds calcul 1877 4500 +ds calcul 1878 4500 +ds calcul 1879 4500 +ds calcul 1880 4500 diff --git a/experiments/resultat16.txt b/experiments/resultat16.txt new file mode 100644 index 0000000..4756d1d --- /dev/null +++ b/experiments/resultat16.txt @@ -0,0 +1,27 @@ +[13, 14, 15, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0] +[13, 14, 15, 8, 11, 10, 9, 12, 7, 6, 5, 4, 3, 2, 1, 0] +[5, 14, 15, 12, 11, 10, 9, 8, 15, 6, 5, 4, 3, 2, 1, 0] +[13, 12, 15, 10, 11, 10, 9, 12, 7, 6, 5, 4, 3, 2, 1, 0] +[13, 14, 15, 8, 11, 10, 9, 12, 7, 6, 4, 5, 3, 2, 1, 0] +[13, 14, 14, 9, 11, 10, 9, 12, 7, 6, 5, 4, 3, 2, 1, 0] +[13, 14, 5, 12, 11, 10, 9, 8, 14, 7, 7, 4, 3, 2, 1, 0] +[13, 14, 5, 12, 11, 10, 9, 8, 15, 7, 4, 6, 3, 2, 1, 0] +[4, 15, 15, 12, 11, 10, 9, 8, 15, 6, 5, 4, 3, 2, 1, 0] +[13, 12, 15, 10, 11, 10, 9, 12, 7, 6, 5, 4, 3, 0, 1, 2] +[13, 4, 15, 10, 11, 10, 9, 12, 7, 14, 5, 4, 3, 2, 1, 0] +[13, 12, 15, 0, 11, 10, 9, 12, 7, 14, 5, 6, 3, 2, 1, 0] +[5, 12, 15, 10, 11, 10, 9, 12, 15, 6, 5, 4, 3, 2, 1, 0] +[13, 12, 15, 2, 11, 10, 9, 12, 7, 6, 5, 12, 3, 2, 1, 0] + + + +[7, 14, 13, 12, 11, 10, 9, 8, 15, 6, 5, 4, 3, 2, 1, 0] +[6, 15, 13, 12, 11, 10, 9, 8, 15, 6, 5, 4, 3, 2, 1, 0] +[7, 15, 13, 12, 11, 10, 9, 8, 6, 14, 5, 4, 3, 2, 1, 0] +[7, 6, 13, 12, 11, 10, 9, 8, 15, 14, 5, 4, 3, 2, 1, 0] +[7, 12, 13, 14, 11, 10, 9, 8, 15, 6, 5, 4, 3, 2, 1, 0] +[7, 14, 13, 4, 11, 10, 9, 8, 15, 6, 5, 12, 3, 2, 1, 0] +[7, 14, 13, 8, 11, 10, 9, 12, 15, 6, 5, 4, 3, 2, 1, 0] +[7, 14, 13, 12, 11, 10, 9, 0, 15, 6, 5, 4, 3, 2, 1, 8] + + diff --git a/experiments/resultat8 b/experiments/resultat8 new file mode 100644 index 0000000..3124dd6 --- /dev/null +++ b/experiments/resultat8 @@ -0,0 +1,4 @@ +------ +[4, 5, 6, 7, 3, 2, 1, 0] +[4, 5, 6, 7, 2, 3, 1, 0] +[4, 5, 6, 7, 2, 0, 3, 1] diff --git a/experiments/resultat8.txt b/experiments/resultat8.txt new file mode 100644 index 0000000..e69de29 diff --git a/experiments/smm.pl b/experiments/smm.pl new file mode 100644 index 0000000..e250541 --- /dev/null +++ b/experiments/smm.pl @@ -0,0 +1,128 @@ +:-use_module(library(clpfd)). + + +% N is the dot product of lists V1 and V2. +dot(V1, V2, N) :- maplist(product,V1,V2,P), sumlist(P,N). +product(N1,N2,N3) :- N3 is N1*N2. + +% Matrix multiplication with matrices represented +% as lists of lists. M3 is the product of M1 and M2 +mmult(M1, M2, M3) :- transpose(M2,MT), maplist(mm_helper(MT), M1, M3). +mm_helper(M2, I1, M3) :- maplist(dot(I1), M2, M3). + + +suml([],[],[]). + +suml(L1,L2,[E1 + E2|R2]):- + L1 = [E1|T1], + L2 = [E2|T2], + suml(T1,T2,R2). + + + +summ([],[],[]). +summ(M1,M2,[Lr|R2]):- + M1 = [E1|T1], + M2 = [E2|T2], + suml(E1,E2,Lr), + summ(T1,T2,R2). + + +flatten(List, Flattened):- + flatten(List, [], Flattened). + +flatten([], Flattened, Flattened). +flatten([Item|Tail], L, Flattened):- + flatten(Item, L1, Flattened), + flatten(Tail, L, L1). +flatten(Item, Flattened, [Item|Flattened]):- + \+ is_list(Item). + +touspositifs(X):- + flatten(X,XF), + tp(XF). + +tp([]). +tp(X):- + X = [E|L], + E #> 0, + tp(L). + + + + + + +sc3(X):- + mmult(X,X,X2), + mmult(X,X2,X3), + mmult(X,X3,X4), + mmult(X,X4,X6), + mmult(X,X4,X6), + mmult(X,X6,X7), + mmult(X,X7,X8), + summ(X,X2,S1), + summ(S1,X3,S2), + summ(S2,X4,S3), + summ(S3,X5,S4), + summ(S4,X6,S5), + summ(S5,X7,S6), + summ(S6,X8,S7), + touspositifs(S7). + +sc2(X):- + mmult(X,X,X2), + mmult(X,X2,X3), + mmult(X,X3,X4), + summ(X,X2,S1), + summ(S1,X3,S2), + summ(S2,X4,S3), + touspositifs(S3). + + + + + +bistoc(X):- + X=[[A,B,C,0],[F,E,0,G],[H,0,I,J],[0,K,L,M]], + A in 0..2, + E in 0..2, + I in 0..2, + M in 0..2, + B in 0..1, + C in 0..1, + F in 0..1, + G in 0..1, + H in 0..1, + J in 0..1, + K in 0..1, + L in 0..1, + A + B + C #= 2, + E + F+ G #= 2, + H+ I+ J#= 2, + K+L +M #= 2, + A+F + H#= 2, + B+E +K #= 2, + C+I + L#= 2, + G+ J+M #= 2, + label([A,B,C,F,E,G,H,I,J,K,L,M]), + sc2(X). + + +display_m([]). +display_m([El|R]):- + write(El), + display_m(R). + + +solution(L):- + get_time(T0), + findall(X,bistoc(X),L), + get_time(T1), + DT is T1 - T0, + write('but : '),writeln(DT), + display_m(L). + + + + diff --git a/experiments/smm2.pl b/experiments/smm2.pl new file mode 100644 index 0000000..ea6a95e --- /dev/null +++ b/experiments/smm2.pl @@ -0,0 +1,116 @@ +:-use_module(library(clpfd)). + + +% N is the dot product of lists V1 and V2. +dot(V1, V2, N) :- maplist(product,V1,V2,P), sumlist(P,N). +product(N1,N2,N3) :- N3 is N1*N2. + +% Matrix multiplication with matrices represented +% as lists of lists. M3 is the product of M1 and M2 +mmult(M1, M2, M3) :- transpose(M2,MT), maplist(mm_helper(MT), M1, M3). +mm_helper(M2, I1, M3) :- maplist(dot(I1), M2, M3). + + +suml([],[],[]). + +suml(L1,L2,[E1 + E2|R2]):- + L1 = [E1|T1], + L2 = [E2|T2], + suml(T1,T2,R2). + + + +summ([],[],[]). +summ(M1,M2,[Lr|R2]):- + M1 = [E1|T1], + M2 = [E2|T2], + suml(E1,E2,Lr), + summ(T1,T2,R2). + + +flatten(List, Flattened):- + flatten(List, [], Flattened). + +flatten([], Flattened, Flattened). +flatten([Item|Tail], L, Flattened):- + flatten(Item, L1, Flattened), + flatten(Tail, L, L1). +flatten(Item, Flattened, [Item|Flattened]):- + \+ is_list(Item). + +touspositifs(X):- + flatten(X,XF), + tp(XF). + +tp([]). +tp(X):- + X = [E|L], + E #> 0, + tp(L). + + + + +sc2(X):- + mmult(X,X,X2), + mmult(X,X2,X3), + mmult(X,X3,X4), + summ(X,X2,S1), + summ(S1,X3,S2), + summ(S2,X4,S3), + touspositifs(S3). + + + + + +bistoc(X):- + X=[[A,B,C,0],[F,E,0,G],[H,0,I,J],[0,K,L,M]], + A in 0..2, + E in 0..2, + I in 0..2, + M in 0..2, + B in 0..1, + C in 0..1, + F in 0..1, + G in 0..1, + H in 0..1, + J in 0..1, + K in 0..1, + L in 0..1, + A + B + C #= 2, + E + F+ G #= 2, + H+ I+ J#= 2, + K+L +M #= 2, + A+F + H#= 2, + B+E +K #= 2, + C+I + L#= 2, + G+ J+M #= 2, + label([A,B,C,F,E,G,H,I,J,K,L,M]), + sc2(X), + open('res2.txt',append,Stream), + write(Stream,X), + close(Stream). + + +display_m([]). +display_m([El|R]):- + write(El), + display_m(R). + + +solution(L):- + get_time(T0), + findall(X,bistoc(X),L), + get_time(T1), + DT is T1 - T0, + write('but : '),writeln(DT). + + + + + + + + + diff --git a/experiments/smm2bis.pl b/experiments/smm2bis.pl new file mode 100644 index 0000000..554f442 --- /dev/null +++ b/experiments/smm2bis.pl @@ -0,0 +1,110 @@ +:-use_module(library(clpfd)). + + +% N is the dot product of lists V1 and V2. +dot(V1, V2, N) :- maplist(product,V1,V2,P), sumlist(P,N). +product(N1,N2,N3) :- N3 is N1*N2. + +% Matrix multiplication with matrices represented +% as lists of lists. M3 is the product of M1 and M2 +mmult(M1, M2, M3) :- transpose(M2,MT), maplist(mm_helper(MT), M1, M3). +mm_helper(M2, I1, M3) :- maplist(dot(I1), M2, M3). + + +suml([],[],[]). + +suml(L1,L2,[E1 + E2|R2]):- + L1 = [E1|T1], + L2 = [E2|T2], + suml(T1,T2,R2). + + + +summ([],[],[]). +summ(M1,M2,[Lr|R2]):- + M1 = [E1|T1], + M2 = [E2|T2], + suml(E1,E2,Lr), + summ(T1,T2,R2). + + +flatten(List, Flattened):- + flatten(List, [], Flattened). + +flatten([], Flattened, Flattened). +flatten([Item|Tail], L, Flattened):- + flatten(Item, L1, Flattened), + flatten(Tail, L, L1). +flatten(Item, Flattened, [Item|Flattened]):- + \+ is_list(Item). + +touspositifs(X):- + flatten(X,XF), + tp(XF). + +tp([]). +tp(X):- + X = [E|L], + E #> 0, + tp(L). + + + + +sc2(X):- + mmult(X,X,X2), + mmult(X,X2,X3), + mmult(X,X3,X4), + summ(X,X2,S1), + summ(S1,X3,S2), + summ(S2,X4,S3), + touspositifs(S3). + + + + + +bistoc(M):- + M=[[M0_0, M0_1, 0, M0_3], [M1_0, M1_1, 0, M1_3], + [M2_0, 0, M2_2, M2_3], [0, M3_1, M3_2, M3_3]], + [M0_0, M1_1, M2_2, M3_3] ins 0..2, + [M0_1, M0_3, M1_0, M1_3, M2_0, M2_3, M3_1, M3_2] ins 0..1, + M0_0+ M0_1+ M0_2 #=2, M1_0+ M1_1+ M1_3 #=2, + M2_0+ M2_2+ M2_3 #=2, M3_1+ M3_2+ M3_3 #=2, + M0_0+ M1_0+ M2_0 #=2, M0_1+ M1_1+ M3_1 #=2, + M0_2+ M2_2+ M3_2 #=2, M1_3+ M2_3+ M3_3 #=2, + mmult(M,M,M2), + mmult(M,M2,M3), + mmult(M,M3,M4), + summ(M,M2,S2), + summ(S2,M3,S3), + summ(S3,M4,S4), + allpositive(S4), + label([M0_0, M0_1, M0_3, M1_0, M1_1, M1_3, M2_0, M2_2, M2_3, M3_1, M3_2, M3_3]), + + open('res2.txt',append,Stream), + write(Stream,M), + close(Stream). + + +display_m([]). +display_m([El|R]):- + write(El), + display_m(R). + + +solution(L):- + get_time(T0), + findall(X,bistoc(X),L), + get_time(T1), + DT is T1 - T0, + write('but : '),writeln(DT). + + + + + + + + + diff --git a/experiments/smm3.pl b/experiments/smm3.pl new file mode 100644 index 0000000..d73a749 --- /dev/null +++ b/experiments/smm3.pl @@ -0,0 +1,184 @@ +:-use_module(library(clpfd)). + + +% N is the dot product of lists V1 and V2. +dot(V1, V2, N) :- maplist(product,V1,V2,P), sumlist(P,N). +product(N1,N2,N3) :- N3 is N1*N2. + +% Matrix multiplication with matrices represented +% as lists of lists. M3 is the product of M1 and M2 +mmult(M1, M2, M3) :- transpose(M2,MT), maplist(mm_helper(MT), M1, M3). +mm_helper(M2, I1, M3) :- maplist(dot(I1), M2, M3). + + +suml([],[],[]). + +suml(L1,L2,[E1 + E2|R2]):- + L1 = [E1|T1], + L2 = [E2|T2], + suml(T1,T2,R2). + + + +summ([],[],[]). +summ(M1,M2,[Lr|R2]):- + M1 = [E1|T1], + M2 = [E2|T2], + suml(E1,E2,Lr), + summ(T1,T2,R2). + + +flatten(List, Flattened):- + flatten(List, [], Flattened). + +flatten([], Flattened, Flattened). +flatten([Item|Tail], L, Flattened):- + flatten(Item, L1, Flattened), + flatten(Tail, L, L1). +flatten(Item, Flattened, [Item|Flattened]):- + \+ is_list(Item). + +touspositifs(X):- + flatten(X,XF), + tp(XF). + +tp([]). +tp(X):- + X = [E|L], + E #> 0, + tp(L). + + +sc3(X1):- + mmult(X1,X1,X2), + mmult(X1,X2,X3), + mmult(X1,X3,X4), + mmult(X1,X4,X5), + mmult(X1,X5,X6), + mmult(X1,X6,X7), + mmult(X1,X7,X8), + summ(X1,X2,S2), + summ(S2,X3,S3), + summ(S3,X4,S4), + summ(S4,X5,S5), + summ(S5,X6,S6), + summ(S6,X7,S7), + summ(S7,X8,S8), + touspositifs(S8). + +bistoc(X):- + X=[[M0X0, M0X1, M0X2, M0X3, M0X4, M0X5, M0X6, M0X7], [M1X0, M1X1, M1X2, M1X3, M1X4, M1X5, M1X6, M1X7], [M2X0, M2X1, M2X2, M2X3, M2X4, M2X5, M2X6, M2X7], [M3X0, M3X1, M3X2, M3X3, M3X4, M3X5, M3X6, M3X7], [M4X0, M4X1, M4X2, M4X3, M4X4, M4X5, M4X6, M4X7], [M5X0, M5X1, M5X2, M5X3, M5X4, M5X5, M5X6, M5X7], [M6X0, M6X1, M6X2, M6X3, M6X4, M6X5, M6X6, M6X7], [M7X0, M7X1, M7X2, M7X3, M7X4, M7X5, M7X6, M7X7]], + M0X0 in 0..3, + M0X1 in 0..1, + M0X2 in 0..1, + M0X3 is 0 , + M0X4 in 0..1, + M0X5 is 0 , + M0X6 is 0 , + M0X7 is 0 , + M1X0 in 0..1, + M1X1 in 0..3, + M1X2 is 0 , + M1X3 in 0..1, + M1X4 is 0 , + M1X5 in 0..1, + M1X6 is 0 , + M1X7 is 0 , + M2X0 in 0..1, + M2X1 is 0 , + M2X2 in 0..3, + M2X3 in 0..1, + M2X4 is 0 , + M2X5 is 0 , + M2X6 in 0..1, + M2X7 is 0 , + M3X0 is 0 , + M3X1 in 0..1, + M3X2 in 0..1, + M3X3 in 0..3, + M3X4 is 0 , + M3X5 is 0 , + M3X6 is 0 , + M3X7 in 0..1, + M4X0 in 0..1, + M4X1 is 0 , + M4X2 is 0 , + M4X3 is 0 , + M4X4 in 0..3, + M4X5 in 0..1, + M4X6 in 0..1, + M4X7 is 0 , + M5X0 is 0 , + M5X1 in 0..1, + M5X2 is 0 , + M5X3 is 0 , + M5X4 in 0..1, + M5X5 in 0..3, + M5X6 is 0 , + M5X7 in 0..1, + M6X0 is 0 , + M6X1 is 0 , + M6X2 in 0..1, + M6X3 is 0 , + M6X4 in 0..1, + M6X5 is 0 , + M6X6 in 0..3, + M6X7 in 0..1, + M7X0 is 0 , + M7X1 is 0 , + M7X2 is 0 , + M7X3 in 0..1, + M7X4 is 0 , + M7X5 in 0..1, + M7X6 in 0..1, + M7X7 in 0..3, + M0X0+ M0X1+ M0X2+ M0X3+ M0X4+ M0X5+ M0X6+ M0X7 #=3 , + M1X0+ M1X1+ M1X2+ M1X3+ M1X4+ M1X5+ M1X6+ M1X7 #=3 , + M2X0+ M2X1+ M2X2+ M2X3+ M2X4+ M2X5+ M2X6+ M2X7 #=3 , + M3X0+ M3X1+ M3X2+ M3X3+ M3X4+ M3X5+ M3X6+ M3X7 #=3 , + M4X0+ M4X1+ M4X2+ M4X3+ M4X4+ M4X5+ M4X6+ M4X7 #=3 , + M5X0+ M5X1+ M5X2+ M5X3+ M5X4+ M5X5+ M5X6+ M5X7 #=3 , + M6X0+ M6X1+ M6X2+ M6X3+ M6X4+ M6X5+ M6X6+ M6X7 #=3 , + M7X0+ M7X1+ M7X2+ M7X3+ M7X4+ M7X5+ M7X6+ M7X7 #=3 , + M0X0+ M0X1+ M0X2+ M0X3+ M0X4+ M0X5+ M0X6+ M0X7 #=3 , + M0X0+ M1X0+ M2X0+ M3X0+ M4X0+ M5X0+ M6X0+ M7X0 #=3 , + M1X0+ M1X1+ M1X2+ M1X3+ M1X4+ M1X5+ M1X6+ M1X7 #=3 , + M0X1+ M1X1+ M2X1+ M3X1+ M4X1+ M5X1+ M6X1+ M7X1 #=3 , + M2X0+ M2X1+ M2X2+ M2X3+ M2X4+ M2X5+ M2X6+ M2X7 #=3 , + M0X2+ M1X2+ M2X2+ M3X2+ M4X2+ M5X2+ M6X2+ M7X2 #=3 , + M3X0+ M3X1+ M3X2+ M3X3+ M3X4+ M3X5+ M3X6+ M3X7 #=3 , + M0X3+ M1X3+ M2X3+ M3X3+ M4X3+ M5X3+ M6X3+ M7X3 #=3 , + M4X0+ M4X1+ M4X2+ M4X3+ M4X4+ M4X5+ M4X6+ M4X7 #=3 , + M0X4+ M1X4+ M2X4+ M3X4+ M4X4+ M5X4+ M6X4+ M7X4 #=3 , + M5X0+ M5X1+ M5X2+ M5X3+ M5X4+ M5X5+ M5X6+ M5X7 #=3 , + M0X5+ M1X5+ M2X5+ M3X5+ M4X5+ M5X5+ M6X5+ M7X5 #=3 , + M6X0+ M6X1+ M6X2+ M6X3+ M6X4+ M6X5+ M6X6+ M6X7 #=3 , + M0X6+ M1X6+ M2X6+ M3X6+ M4X6+ M5X6+ M6X6+ M7X6 #=3 , + M7X0+ M7X1+ M7X2+ M7X3+ M7X4+ M7X5+ M7X6+ M7X7 #=3 , + M0X7+ M1X7+ M2X7+ M3X7+ M4X7+ M5X7+ M6X7+ M7X7 #=3 , + label([M0X0, M0X1, M0X2, M0X3, M0X4, M0X5, M0X6, M0X7, M1X0, M1X1, M1X2, M1X3, M1X4, M1X5, M1X6, M1X7, M2X0, M2X1, M2X2, M2X3, M2X4, M2X5, M2X6, M2X7, M3X0, M3X1, M3X2, M3X3, M3X4, M3X5, M3X6, M3X7, M4X0, M4X1, M4X2, M4X3, M4X4, M4X5, M4X6, M4X7, M5X0, M5X1, M5X2, M5X3, M5X4, M5X5, M5X6, M5X7, M6X0, M6X1, M6X2, M6X3, M6X4, M6X5, M6X6, M6X7, M7X0, M7X1, M7X2, M7X3, M7X4, M7X5, M7X6, M7X7]), + sc3(X), + open('res3.txt',append,Stream), + write(Stream,X), + close(Stream). + + + + +display_m([]). +display_m([El|R]):- + write(El), + display_m(R). + + +solution(L):- + get_time(T0), + findall(X,bistoc(X),L), + get_time(T1), + DT is T1 - T0, + write('but : '),writeln(DT), + display_m(L). + + + + diff --git a/experiments/smm4.pl b/experiments/smm4.pl new file mode 100644 index 0000000..f40afca --- /dev/null +++ b/experiments/smm4.pl @@ -0,0 +1,417 @@ +:-use_module(library(clpfd)). + + +% N is the dot product of lists V1 and V2. +dot(V1, V2, N) :- maplist(product,V1,V2,P), sumlist(P,N). +product(N1,N2,N3) :- N3 is N1*N2. + +% Matrix multiplication with matrices represented +% as lists of lists. M3 is the product of M1 and M2 +mmult(M1, M2, M3) :- transpose(M2,MT), maplist(mm_helper(MT), M1, M3). +mm_helper(M2, I1, M3) :- maplist(dot(I1), M2, M3). + + +suml([],[],[]). + +suml(L1,L2,[E1 + E2|R2]):- + L1 = [E1|T1], + L2 = [E2|T2], + suml(T1,T2,R2). + + + +summ([],[],[]). +summ(M1,M2,[Lr|R2]):- + M1 = [E1|T1], + M2 = [E2|T2], + suml(E1,E2,Lr), + summ(T1,T2,R2). + + +flatten(List, Flattened):- + flatten(List, [], Flattened). + +flatten([], Flattened, Flattened). +flatten([Item|Tail], L, Flattened):- + flatten(Item, L1, Flattened), + flatten(Tail, L, L1). +flatten(Item, Flattened, [Item|Flattened]):- + \+ is_list(Item). + +touspositifs(X):- + flatten(X,XF), + tp(XF). + +tp([]). +tp(X):- + X = [E|L], + E #> 0, + tp(L). + + +sc4(X1):- + mmult(X1,X1,X2), + mmult(X1,X2,X3), + mmult(X1,X3,X4), + mmult(X1,X4,X5), + mmult(X1,X5,X6), + mmult(X1,X6,X7), + mmult(X1,X7,X8), + mmult(X1,X8,X9), + mmult(X1,X9,X10), + mmult(X1,X10,X11), + mmult(X1,X11,X12), + mmult(X1,X12,X13), + mmult(X1,X13,X14), + mmult(X1,X14,X15), + mmult(X1,X15,X16), + summ(X1,X2,S2), + summ(S2,X3,S3), + summ(S3,X4,S4), + summ(S4,X5,S5), + summ(S5,X6,S6), + summ(S6,X7,S7), + summ(S7,X8,S8), + summ(S8,X9,S9), + summ(S9,X10,S10), + summ(S10,X11,S11), + summ(S11,X12,S12), + summ(S12,X13,S13), + summ(S13,X14,S14), + summ(S14,X15,S15), + summ(S15,X16,S16), + touspositifs(S16). + +bistoc(X):- + X=[[M0X0, M0X1, M0X2, M0X3, M0X4, M0X5, M0X6, M0X7, M0X8, M0X9, M0X10, M0X11, M0X12, M0X13, M0X14, M0X15], [M1X0, M1X1, M1X2, M1X3, M1X4, M1X5, M1X6, M1X7, M1X8, M1X9, M1X10, M1X11, M1X12, M1X13, M1X14, M1X15], [M2X0, M2X1, M2X2, M2X3, M2X4, M2X5, M2X6, M2X7, M2X8, M2X9, M2X10, M2X11, M2X12, M2X13, M2X14, M2X15], [M3X0, M3X1, M3X2, M3X3, M3X4, M3X5, M3X6, M3X7, M3X8, M3X9, M3X10, M3X11, M3X12, M3X13, M3X14, M3X15], [M4X0, M4X1, M4X2, M4X3, M4X4, M4X5, M4X6, M4X7, M4X8, M4X9, M4X10, M4X11, M4X12, M4X13, M4X14, M4X15], [M5X0, M5X1, M5X2, M5X3, M5X4, M5X5, M5X6, M5X7, M5X8, M5X9, M5X10, M5X11, M5X12, M5X13, M5X14, M5X15], [M6X0, M6X1, M6X2, M6X3, M6X4, M6X5, M6X6, M6X7, M6X8, M6X9, M6X10, M6X11, M6X12, M6X13, M6X14, M6X15], [M7X0, M7X1, M7X2, M7X3, M7X4, M7X5, M7X6, M7X7, M7X8, M7X9, M7X10, M7X11, M7X12, M7X13, M7X14, M7X15], [M8X0, M8X1, M8X2, M8X3, M8X4, M8X5, M8X6, M8X7, M8X8, M8X9, M8X10, M8X11, M8X12, M8X13, M8X14, M8X15], [M9X0, M9X1, M9X2, M9X3, M9X4, M9X5, M9X6, M9X7, M9X8, M9X9, M9X10, M9X11, M9X12, M9X13, M9X14, M9X15], [M10X0, M10X1, M10X2, M10X3, M10X4, M10X5, M10X6, M10X7, M10X8, M10X9, M10X10, M10X11, M10X12, M10X13, M10X14, M10X15], [M11X0, M11X1, M11X2, M11X3, M11X4, M11X5, M11X6, M11X7, M11X8, M11X9, M11X10, M11X11, M11X12, M11X13, M11X14, M11X15], [M12X0, M12X1, M12X2, M12X3, M12X4, M12X5, M12X6, M12X7, M12X8, M12X9, M12X10, M12X11, M12X12, M12X13, M12X14, M12X15], [M13X0, M13X1, M13X2, M13X3, M13X4, M13X5, M13X6, M13X7, M13X8, M13X9, M13X10, M13X11, M13X12, M13X13, M13X14, M13X15], [M14X0, M14X1, M14X2, M14X3, M14X4, M14X5, M14X6, M14X7, M14X8, M14X9, M14X10, M14X11, M14X12, M14X13, M14X14, M14X15], [M15X0, M15X1, M15X2, M15X3, M15X4, M15X5, M15X6, M15X7, M15X8, M15X9, M15X10, M15X11, M15X12, M15X13, M15X14, M15X15]], + M0X0 in 0..4, + M0X1 in 0..1, + M0X2 in 0..1, + M0X3 is 0 , + M0X4 in 0..1, + M0X5 is 0 , + M0X6 is 0 , + M0X7 is 0 , + M0X8 in 0..1, + M0X9 is 0 , + M0X10 is 0 , + M0X11 is 0 , + M0X12 is 0 , + M0X13 is 0 , + M0X14 is 0 , + M0X15 is 0 , + M1X0 in 0..1, + M1X1 in 0..4, + M1X2 is 0 , + M1X3 in 0..1, + M1X4 is 0 , + M1X5 in 0..1, + M1X6 is 0 , + M1X7 is 0 , + M1X8 is 0 , + M1X9 in 0..1, + M1X10 is 0 , + M1X11 is 0 , + M1X12 is 0 , + M1X13 is 0 , + M1X14 is 0 , + M1X15 is 0 , + M2X0 in 0..1, + M2X1 is 0 , + M2X2 in 0..4, + M2X3 in 0..1, + M2X4 is 0 , + M2X5 is 0 , + M2X6 in 0..1, + M2X7 is 0 , + M2X8 is 0 , + M2X9 is 0 , + M2X10 in 0..1, + M2X11 is 0 , + M2X12 is 0 , + M2X13 is 0 , + M2X14 is 0 , + M2X15 is 0 , + M3X0 is 0 , + M3X1 in 0..1, + M3X2 in 0..1, + M3X3 in 0..4, + M3X4 is 0 , + M3X5 is 0 , + M3X6 is 0 , + M3X7 in 0..1, + M3X8 is 0 , + M3X9 is 0 , + M3X10 is 0 , + M3X11 in 0..1, + M3X12 is 0 , + M3X13 is 0 , + M3X14 is 0 , + M3X15 is 0 , + M4X0 in 0..1, + M4X1 is 0 , + M4X2 is 0 , + M4X3 is 0 , + M4X4 in 0..4, + M4X5 in 0..1, + M4X6 in 0..1, + M4X7 is 0 , + M4X8 is 0 , + M4X9 is 0 , + M4X10 is 0 , + M4X11 is 0 , + M4X12 in 0..1, + M4X13 is 0 , + M4X14 is 0 , + M4X15 is 0 , + M5X0 is 0 , + M5X1 in 0..1, + M5X2 is 0 , + M5X3 is 0 , + M5X4 in 0..1, + M5X5 in 0..4, + M5X6 is 0 , + M5X7 in 0..1, + M5X8 is 0 , + M5X9 is 0 , + M5X10 is 0 , + M5X11 is 0 , + M5X12 is 0 , + M5X13 in 0..1, + M5X14 is 0 , + M5X15 is 0 , + M6X0 is 0 , + M6X1 is 0 , + M6X2 in 0..1, + M6X3 is 0 , + M6X4 in 0..1, + M6X5 is 0 , + M6X6 in 0..4, + M6X7 in 0..1, + M6X8 is 0 , + M6X9 is 0 , + M6X10 is 0 , + M6X11 is 0 , + M6X12 is 0 , + M6X13 is 0 , + M6X14 in 0..1, + M6X15 is 0 , + M7X0 is 0 , + M7X1 is 0 , + M7X2 is 0 , + M7X3 in 0..1, + M7X4 is 0 , + M7X5 in 0..1, + M7X6 in 0..1, + M7X7 in 0..4, + M7X8 is 0 , + M7X9 is 0 , + M7X10 is 0 , + M7X11 is 0 , + M7X12 is 0 , + M7X13 is 0 , + M7X14 is 0 , + M7X15 in 0..1, + M8X0 in 0..1, + M8X1 is 0 , + M8X2 is 0 , + M8X3 is 0 , + M8X4 is 0 , + M8X5 is 0 , + M8X6 is 0 , + M8X7 is 0 , + M8X8 in 0..4, + M8X9 in 0..1, + M8X10 in 0..1, + M8X11 is 0 , + M8X12 in 0..1, + M8X13 is 0 , + M8X14 is 0 , + M8X15 is 0 , + M9X0 is 0 , + M9X1 in 0..1, + M9X2 is 0 , + M9X3 is 0 , + M9X4 is 0 , + M9X5 is 0 , + M9X6 is 0 , + M9X7 is 0 , + M9X8 in 0..1, + M9X9 in 0..4, + M9X10 is 0 , + M9X11 in 0..1, + M9X12 is 0 , + M9X13 in 0..1, + M9X14 is 0 , + M9X15 is 0 , + M10X0 is 0 , + M10X1 is 0 , + M10X2 in 0..1, + M10X3 is 0 , + M10X4 is 0 , + M10X5 is 0 , + M10X6 is 0 , + M10X7 is 0 , + M10X8 in 0..1, + M10X9 is 0 , + M10X10 in 0..4, + M10X11 in 0..1, + M10X12 is 0 , + M10X13 is 0 , + M10X14 in 0..1, + M10X15 is 0 , + M11X0 is 0 , + M11X1 is 0 , + M11X2 is 0 , + M11X3 in 0..1, + M11X4 is 0 , + M11X5 is 0 , + M11X6 is 0 , + M11X7 is 0 , + M11X8 is 0 , + M11X9 in 0..1, + M11X10 in 0..1, + M11X11 in 0..4, + M11X12 is 0 , + M11X13 is 0 , + M11X14 is 0 , + M11X15 in 0..1, + M12X0 is 0 , + M12X1 is 0 , + M12X2 is 0 , + M12X3 is 0 , + M12X4 in 0..1, + M12X5 is 0 , + M12X6 is 0 , + M12X7 is 0 , + M12X8 in 0..1, + M12X9 is 0 , + M12X10 is 0 , + M12X11 is 0 , + M12X12 in 0..4, + M12X13 in 0..1, + M12X14 in 0..1, + M12X15 is 0 , + M13X0 is 0 , + M13X1 is 0 , + M13X2 is 0 , + M13X3 is 0 , + M13X4 is 0 , + M13X5 in 0..1, + M13X6 is 0 , + M13X7 is 0 , + M13X8 is 0 , + M13X9 in 0..1, + M13X10 is 0 , + M13X11 is 0 , + M13X12 in 0..1, + M13X13 in 0..4, + M13X14 is 0 , + M13X15 in 0..1, + M14X0 is 0 , + M14X1 is 0 , + M14X2 is 0 , + M14X3 is 0 , + M14X4 is 0 , + M14X5 is 0 , + M14X6 in 0..1, + M14X7 is 0 , + M14X8 is 0 , + M14X9 is 0 , + M14X10 in 0..1, + M14X11 is 0 , + M14X12 in 0..1, + M14X13 is 0 , + M14X14 in 0..4, + M14X15 in 0..1, + M15X0 is 0 , + M15X1 is 0 , + M15X2 is 0 , + M15X3 is 0 , + M15X4 is 0 , + M15X5 is 0 , + M15X6 is 0 , + M15X7 in 0..1, + M15X8 is 0 , + M15X9 is 0 , + M15X10 is 0 , + M15X11 in 0..1, + M15X12 is 0 , + M15X13 in 0..1, + M15X14 in 0..1, + M15X15 in 0..4, + M0X0+ M0X1+ M0X2+ M0X3+ M0X4+ M0X5+ M0X6+ M0X7+ M0X8+ M0X9+ M0X10+ M0X11+ M0X12+ M0X13+ M0X14+ M0X15 #=4 , + M1X0+ M1X1+ M1X2+ M1X3+ M1X4+ M1X5+ M1X6+ M1X7+ M1X8+ M1X9+ M1X10+ M1X11+ M1X12+ M1X13+ M1X14+ M1X15 #=4 , + M2X0+ M2X1+ M2X2+ M2X3+ M2X4+ M2X5+ M2X6+ M2X7+ M2X8+ M2X9+ M2X10+ M2X11+ M2X12+ M2X13+ M2X14+ M2X15 #=4 , + M3X0+ M3X1+ M3X2+ M3X3+ M3X4+ M3X5+ M3X6+ M3X7+ M3X8+ M3X9+ M3X10+ M3X11+ M3X12+ M3X13+ M3X14+ M3X15 #=4 , + M4X0+ M4X1+ M4X2+ M4X3+ M4X4+ M4X5+ M4X6+ M4X7+ M4X8+ M4X9+ M4X10+ M4X11+ M4X12+ M4X13+ M4X14+ M4X15 #=4 , + M5X0+ M5X1+ M5X2+ M5X3+ M5X4+ M5X5+ M5X6+ M5X7+ M5X8+ M5X9+ M5X10+ M5X11+ M5X12+ M5X13+ M5X14+ M5X15 #=4 , + M6X0+ M6X1+ M6X2+ M6X3+ M6X4+ M6X5+ M6X6+ M6X7+ M6X8+ M6X9+ M6X10+ M6X11+ M6X12+ M6X13+ M6X14+ M6X15 #=4 , + M7X0+ M7X1+ M7X2+ M7X3+ M7X4+ M7X5+ M7X6+ M7X7+ M7X8+ M7X9+ M7X10+ M7X11+ M7X12+ M7X13+ M7X14+ M7X15 #=4 , + M8X0+ M8X1+ M8X2+ M8X3+ M8X4+ M8X5+ M8X6+ M8X7+ M8X8+ M8X9+ M8X10+ M8X11+ M8X12+ M8X13+ M8X14+ M8X15 #=4 , + M9X0+ M9X1+ M9X2+ M9X3+ M9X4+ M9X5+ M9X6+ M9X7+ M9X8+ M9X9+ M9X10+ M9X11+ M9X12+ M9X13+ M9X14+ M9X15 #=4 , + M10X0+ M10X1+ M10X2+ M10X3+ M10X4+ M10X5+ M10X6+ M10X7+ M10X8+ M10X9+ M10X10+ M10X11+ M10X12+ M10X13+ M10X14+ M10X15 #=4 , + M11X0+ M11X1+ M11X2+ M11X3+ M11X4+ M11X5+ M11X6+ M11X7+ M11X8+ M11X9+ M11X10+ M11X11+ M11X12+ M11X13+ M11X14+ M11X15 #=4 , + M12X0+ M12X1+ M12X2+ M12X3+ M12X4+ M12X5+ M12X6+ M12X7+ M12X8+ M12X9+ M12X10+ M12X11+ M12X12+ M12X13+ M12X14+ M12X15 #=4 , + M13X0+ M13X1+ M13X2+ M13X3+ M13X4+ M13X5+ M13X6+ M13X7+ M13X8+ M13X9+ M13X10+ M13X11+ M13X12+ M13X13+ M13X14+ M13X15 #=4 , + M14X0+ M14X1+ M14X2+ M14X3+ M14X4+ M14X5+ M14X6+ M14X7+ M14X8+ M14X9+ M14X10+ M14X11+ M14X12+ M14X13+ M14X14+ M14X15 #=4 , + M15X0+ M15X1+ M15X2+ M15X3+ M15X4+ M15X5+ M15X6+ M15X7+ M15X8+ M15X9+ M15X10+ M15X11+ M15X12+ M15X13+ M15X14+ M15X15 #=4 , + M0X0+ M0X1+ M0X2+ M0X3+ M0X4+ M0X5+ M0X6+ M0X7+ M0X8+ M0X9+ M0X10+ M0X11+ M0X12+ M0X13+ M0X14+ M0X15 #=4 , + M0X0+ M1X0+ M2X0+ M3X0+ M4X0+ M5X0+ M6X0+ M7X0+ M8X0+ M9X0+ M10X0+ M11X0+ M12X0+ M13X0+ M14X0+ M15X0 #=4 , + M1X0+ M1X1+ M1X2+ M1X3+ M1X4+ M1X5+ M1X6+ M1X7+ M1X8+ M1X9+ M1X10+ M1X11+ M1X12+ M1X13+ M1X14+ M1X15 #=4 , + M0X1+ M1X1+ M2X1+ M3X1+ M4X1+ M5X1+ M6X1+ M7X1+ M8X1+ M9X1+ M10X1+ M11X1+ M12X1+ M13X1+ M14X1+ M15X1 #=4 , + M2X0+ M2X1+ M2X2+ M2X3+ M2X4+ M2X5+ M2X6+ M2X7+ M2X8+ M2X9+ M2X10+ M2X11+ M2X12+ M2X13+ M2X14+ M2X15 #=4 , + M0X2+ M1X2+ M2X2+ M3X2+ M4X2+ M5X2+ M6X2+ M7X2+ M8X2+ M9X2+ M10X2+ M11X2+ M12X2+ M13X2+ M14X2+ M15X2 #=4 , + M3X0+ M3X1+ M3X2+ M3X3+ M3X4+ M3X5+ M3X6+ M3X7+ M3X8+ M3X9+ M3X10+ M3X11+ M3X12+ M3X13+ M3X14+ M3X15 #=4 , + M0X3+ M1X3+ M2X3+ M3X3+ M4X3+ M5X3+ M6X3+ M7X3+ M8X3+ M9X3+ M10X3+ M11X3+ M12X3+ M13X3+ M14X3+ M15X3 #=4 , + M4X0+ M4X1+ M4X2+ M4X3+ M4X4+ M4X5+ M4X6+ M4X7+ M4X8+ M4X9+ M4X10+ M4X11+ M4X12+ M4X13+ M4X14+ M4X15 #=4 , + M0X4+ M1X4+ M2X4+ M3X4+ M4X4+ M5X4+ M6X4+ M7X4+ M8X4+ M9X4+ M10X4+ M11X4+ M12X4+ M13X4+ M14X4+ M15X4 #=4 , + M5X0+ M5X1+ M5X2+ M5X3+ M5X4+ M5X5+ M5X6+ M5X7+ M5X8+ M5X9+ M5X10+ M5X11+ M5X12+ M5X13+ M5X14+ M5X15 #=4 , + M0X5+ M1X5+ M2X5+ M3X5+ M4X5+ M5X5+ M6X5+ M7X5+ M8X5+ M9X5+ M10X5+ M11X5+ M12X5+ M13X5+ M14X5+ M15X5 #=4 , + M6X0+ M6X1+ M6X2+ M6X3+ M6X4+ M6X5+ M6X6+ M6X7+ M6X8+ M6X9+ M6X10+ M6X11+ M6X12+ M6X13+ M6X14+ M6X15 #=4 , + M0X6+ M1X6+ M2X6+ M3X6+ M4X6+ M5X6+ M6X6+ M7X6+ M8X6+ M9X6+ M10X6+ M11X6+ M12X6+ M13X6+ M14X6+ M15X6 #=4 , + M7X0+ M7X1+ M7X2+ M7X3+ M7X4+ M7X5+ M7X6+ M7X7+ M7X8+ M7X9+ M7X10+ M7X11+ M7X12+ M7X13+ M7X14+ M7X15 #=4 , + M0X7+ M1X7+ M2X7+ M3X7+ M4X7+ M5X7+ M6X7+ M7X7+ M8X7+ M9X7+ M10X7+ M11X7+ M12X7+ M13X7+ M14X7+ M15X7 #=4 , + M8X0+ M8X1+ M8X2+ M8X3+ M8X4+ M8X5+ M8X6+ M8X7+ M8X8+ M8X9+ M8X10+ M8X11+ M8X12+ M8X13+ M8X14+ M8X15 #=4 , + M0X8+ M1X8+ M2X8+ M3X8+ M4X8+ M5X8+ M6X8+ M7X8+ M8X8+ M9X8+ M10X8+ M11X8+ M12X8+ M13X8+ M14X8+ M15X8 #=4 , + M9X0+ M9X1+ M9X2+ M9X3+ M9X4+ M9X5+ M9X6+ M9X7+ M9X8+ M9X9+ M9X10+ M9X11+ M9X12+ M9X13+ M9X14+ M9X15 #=4 , + M0X9+ M1X9+ M2X9+ M3X9+ M4X9+ M5X9+ M6X9+ M7X9+ M8X9+ M9X9+ M10X9+ M11X9+ M12X9+ M13X9+ M14X9+ M15X9 #=4 , + M10X0+ M10X1+ M10X2+ M10X3+ M10X4+ M10X5+ M10X6+ M10X7+ M10X8+ M10X9+ M10X10+ M10X11+ M10X12+ M10X13+ M10X14+ M10X15 #=4 , + M0X10+ M1X10+ M2X10+ M3X10+ M4X10+ M5X10+ M6X10+ M7X10+ M8X10+ M9X10+ M10X10+ M11X10+ M12X10+ M13X10+ M14X10+ M15X10 #=4 , + M11X0+ M11X1+ M11X2+ M11X3+ M11X4+ M11X5+ M11X6+ M11X7+ M11X8+ M11X9+ M11X10+ M11X11+ M11X12+ M11X13+ M11X14+ M11X15 #=4 , + M0X11+ M1X11+ M2X11+ M3X11+ M4X11+ M5X11+ M6X11+ M7X11+ M8X11+ M9X11+ M10X11+ M11X11+ M12X11+ M13X11+ M14X11+ M15X11 #=4 , + M12X0+ M12X1+ M12X2+ M12X3+ M12X4+ M12X5+ M12X6+ M12X7+ M12X8+ M12X9+ M12X10+ M12X11+ M12X12+ M12X13+ M12X14+ M12X15 #=4 , + M0X12+ M1X12+ M2X12+ M3X12+ M4X12+ M5X12+ M6X12+ M7X12+ M8X12+ M9X12+ M10X12+ M11X12+ M12X12+ M13X12+ M14X12+ M15X12 #=4 , + M13X0+ M13X1+ M13X2+ M13X3+ M13X4+ M13X5+ M13X6+ M13X7+ M13X8+ M13X9+ M13X10+ M13X11+ M13X12+ M13X13+ M13X14+ M13X15 #=4 , + M0X13+ M1X13+ M2X13+ M3X13+ M4X13+ M5X13+ M6X13+ M7X13+ M8X13+ M9X13+ M10X13+ M11X13+ M12X13+ M13X13+ M14X13+ M15X13 #=4 , + M14X0+ M14X1+ M14X2+ M14X3+ M14X4+ M14X5+ M14X6+ M14X7+ M14X8+ M14X9+ M14X10+ M14X11+ M14X12+ M14X13+ M14X14+ M14X15 #=4 , + M0X14+ M1X14+ M2X14+ M3X14+ M4X14+ M5X14+ M6X14+ M7X14+ M8X14+ M9X14+ M10X14+ M11X14+ M12X14+ M13X14+ M14X14+ M15X14 #=4 , + M15X0+ M15X1+ M15X2+ M15X3+ M15X4+ M15X5+ M15X6+ M15X7+ M15X8+ M15X9+ M15X10+ M15X11+ M15X12+ M15X13+ M15X14+ M15X15 #=4 , + M0X15+ M1X15+ M2X15+ M3X15+ M4X15+ M5X15+ M6X15+ M7X15+ M8X15+ M9X15+ M10X15+ M11X15+ M12X15+ M13X15+ M14X15+ M15X15 #=4 , + label([M0X0, M0X1, M0X2, M0X3, M0X4, M0X5, M0X6, M0X7, M0X8, M0X9, M0X10, M0X11, M0X12, M0X13, M0X14, M0X15, M1X0, M1X1, M1X2, M1X3, M1X4, M1X5, M1X6, M1X7, M1X8, M1X9, M1X10, M1X11, M1X12, M1X13, M1X14, M1X15, M2X0, M2X1, M2X2, M2X3, M2X4, M2X5, M2X6, M2X7, M2X8, M2X9, M2X10, M2X11, M2X12, M2X13, M2X14, M2X15, M3X0, M3X1, M3X2, M3X3, M3X4, M3X5, M3X6, M3X7, M3X8, M3X9, M3X10, M3X11, M3X12, M3X13, M3X14, M3X15, M4X0, M4X1, M4X2, M4X3, M4X4, M4X5, M4X6, M4X7, M4X8, M4X9, M4X10, M4X11, M4X12, M4X13, M4X14, M4X15, M5X0, M5X1, M5X2, M5X3, M5X4, M5X5, M5X6, M5X7, M5X8, M5X9, M5X10, M5X11, M5X12, M5X13, M5X14, M5X15, M6X0, M6X1, M6X2, M6X3, M6X4, M6X5, M6X6, M6X7, M6X8, M6X9, M6X10, M6X11, M6X12, M6X13, M6X14, M6X15, M7X0, M7X1, M7X2, M7X3, M7X4, M7X5, M7X6, M7X7, M7X8, M7X9, M7X10, M7X11, M7X12, M7X13, M7X14, M7X15, M8X0, M8X1, M8X2, M8X3, M8X4, M8X5, M8X6, M8X7, M8X8, M8X9, M8X10, M8X11, M8X12, M8X13, M8X14, M8X15, M9X0, M9X1, M9X2, M9X3, M9X4, M9X5, M9X6, M9X7, M9X8, M9X9, M9X10, M9X11, M9X12, M9X13, M9X14, M9X15, M10X0, M10X1, M10X2, M10X3, M10X4, M10X5, M10X6, M10X7, M10X8, M10X9, M10X10, M10X11, M10X12, M10X13, M10X14, M10X15, M11X0, M11X1, M11X2, M11X3, M11X4, M11X5, M11X6, M11X7, M11X8, M11X9, M11X10, M11X11, M11X12, M11X13, M11X14, M11X15, M12X0, M12X1, M12X2, M12X3, M12X4, M12X5, M12X6, M12X7, M12X8, M12X9, M12X10, M12X11, M12X12, M12X13, M12X14, M12X15, M13X0, M13X1, M13X2, M13X3, M13X4, M13X5, M13X6, M13X7, M13X8, M13X9, M13X10, M13X11, M13X12, M13X13, M13X14, M13X15, M14X0, M14X1, M14X2, M14X3, M14X4, M14X5, M14X6, M14X7, M14X8, M14X9, M14X10, M14X11, M14X12, M14X13, M14X14, M14X15, M15X0, M15X1, M15X2, M15X3, M15X4, M15X5, M15X6, M15X7, M15X8, M15X9, M15X10, M15X11, M15X12, M15X13, M15X14, M15X15]), + sc4(X), + open('res4.txt',append,Stream), + write(Stream,X), + close(Stream). + + + + + +display_m([]). +display_m([El|R]):- + write(El), + display_m(R). + + +solution(L):- + get_time(T0), + findall(X,bistoc(X),L), + get_time(T1), + DT is T1 - T0, + write('but : '),writeln(DT), + display_m(L). + + + + diff --git a/experiments/testVP.py b/experiments/testVP.py new file mode 100644 index 0000000..e9d5aec --- /dev/null +++ b/experiments/testVP.py @@ -0,0 +1,4 @@ +import numpy as np + +A = np.zeros(12) +A[0,0] diff --git a/graphe1.pdf b/graphe1.pdf new file mode 100644 index 0000000..0e0e765 Binary files /dev/null and b/graphe1.pdf differ diff --git a/graphe2.pdf b/graphe2.pdf new file mode 100644 index 0000000..9ea5f8e Binary files /dev/null and b/graphe2.pdf differ diff --git a/intro.tex b/intro.tex new file mode 100644 index 0000000..7b342b6 --- /dev/null +++ b/intro.tex @@ -0,0 +1,71 @@ + +From the last two decades, many researchers have investigated the use +of chaotic systems to build pseudorandom +sequences~\cite{915396,915385,5376454}. Two main features can +intuitively explain this interest: first of all, chaotic systems have +unpredictable or disorder-like behavior which is needed for producing +complex sequences. Furthermore, such systems are extremely sensitive +to the initial states too: a tiny difference in the input +may lead to dramatic changes in output. + +Moreover, the property of chaos is often reduced to iterate a +\emph{chaotic} function, namely the logistic map\footnote{The logistic +map is defined by $X^0 \in [0,1], X^{n+1} = \mu X^n(1-X^n), \mu \in +[0,4]$.}~\cite{915396,915385}, the Arnolds cat map\footnote{Discrete +Arnolds cat map is defined by $(X^0, Y^0)\in [0,N]^2, X^{n+1} = 2 Y^n ++ X^n$ mod $N$, $Y^{n+1} = X^n+Y^n$ mod $N$.}~\cite{5376454}\ldots +Au\-thors +are thus focused on finding parameters of such kind of functions which +are the most suitable for generating random-like sequences. More +precisely, they have thus to find function parameters that avoid +parasitic attractors and that lead to a uniform distribution of the +output. To check how accurate are their generated +sequences~\cite{bfgw13:ij}, authors are then left to submit their +chaos-based PRNG with good parameters on statistical batteries of +tests~\cite{DBLP:journals/corr/abs-1112-5239}, namely: +DieHARD~\cite{Marsaglia1996}, NIST~\cite{Nist10}, and +TestU01~\cite{LEcuyerS07}. + + + +Devaney has formalized~\cite{Devaney} the fundamental properties of +the chaotic maps, namely: sensitive dependence on initial conditions, +transitivity, and density of periodic points. For short, a system is +sensitive to initial conditions if any point contains, in any +neighborhood, another point with a completely different future +trajectory. Topological transitivity is established when, for any +element, any neighborhood of its future evolution eventually overlaps +with any other open set. On the contrary, a dense set of periodic +points is an element of regularity that a chaotic dynamical system has +to exhibit. However, because of the finiteness of the memory of a +computer, only a kind of discrete chaos is generated. This induces +that chaotic properties, which could have been proven on $\Reels$, can +however be lost on floating point numbers, which is the interpretation +domain of $\Reels$. + +To avoid this loss of chaos, we had constructed chaos-based PRNGs +that iterate a continuous functions $G_f$ defined on the discrete +domain $\llbracket 1 ; n \rrbracket^{\Nats} \times \{0,1\}^n$ where +$f$ is a Boolean function (\textit{i.e.}, $f : \{0,1\}^n \rightarrow +\{0,1\}^n$). These PRNGs are named +$\textit{CIPRNG}_f^1(u)$~\cite{bgw09:ip,guyeuxTaiwan10}, +$\textit{CIPRNG}_f^2(u,v)$~\cite{wbg10:ip}, and +$\textit{XOR~CIPRNG}(S)$~\cite{DBLP:journals/corr/abs-1112-5239}, +where \textit{CI} stands for \emph{Chaotic Iterations}, which have +been particularized according to the function they iterate. + +Chaotic properties have been well established for both the +$\textit{XOR~CIPRNG}$ and $\textit{CIPRNG}_f^1(u)$ under certain +conditions for the iteration function $f$, it has been formerly +deduced that it was the case too for the whole $\textit{CIPRNG}_f^2$ +category of generators. However, contrarily to what has been too much +rapidly deduced, this claim is not obvious (a subsequence of a chaotic +sequence is not necessarily a chaotic sequence too) and it +necessitates a rigorous proof, which is the aim of this article. + +The remainder of the paper is organized as follows. +Section~\ref{sec:notations} recalls definitions of chaos properties +and of the family of \textit{CIPRNG}. Section~\ref{sec:wellchosen} +gives the complete proof of chaos for the $\textit{CIPRNG}_f^2$ +category. This is the main contribution of this work. The paper ends +with a conclusion section where intended future work is presented. diff --git a/iter_f0-eps-converted-to.pdf b/iter_f0-eps-converted-to.pdf new file mode 100644 index 0000000..2d366f7 Binary files /dev/null and b/iter_f0-eps-converted-to.pdf differ diff --git a/iter_f0.dot b/iter_f0.dot new file mode 100644 index 0000000..5343192 --- /dev/null +++ b/iter_f0.dot @@ -0,0 +1,27 @@ +digraph { + graph [rankdir=LR] + 000 -> 000; + 000 -> 010; + 000 -> 001; + 010 -> 010; + 010 -> 110; + 010 -> 011; + 001 -> 000; + 001 -> 001; + 001 -> 101; + 101 -> 101; + 101 -> 100; + 101 -> 111; + 110 -> 110; + 110 -> 100; + 110 -> 111; + 011 -> 010; + 011 -> 001; + 011 -> 011; + 100 -> 000; + 100 -> 101; + 100 -> 100; + 111 -> 110; + 111 -> 011; + 111 -> 111; +} diff --git a/iter_f0.eps b/iter_f0.eps new file mode 100644 index 0000000..6962b81 --- /dev/null +++ b/iter_f0.eps @@ -0,0 +1,766 @@ +%!PS-Adobe-3.0 +%%Creator: graphviz version 2.36.0 (20140111.2315) +%%Title: %3 +%%Pages: (atend) 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Solidus \/ +%% Colon \: Semicolon \; Less than \< +%% Equals \= Greater than \> Question mark \? +%% Commercial at \@ Left bracket \[ Backslash \\ +%% Right bracket \] Circumflex \^ Underscore \_ +%% Grave accent \` Left brace \{ Vertical bar \| +%% Right brace \} Tilde \~} +%% +\NeedsTeXFormat{LaTeX2e}[1995/12/01] +\ProvidesClass{llncs}[2010/07/12 v2.17 +^^J LaTeX document class for Lecture Notes in Computer Science] +% Options +\let\if@envcntreset\iffalse +\DeclareOption{envcountreset}{\let\if@envcntreset\iftrue} +\DeclareOption{citeauthoryear}{\let\citeauthoryear=Y} +\DeclareOption{oribibl}{\let\oribibl=Y} +\let\if@custvec\iftrue +\DeclareOption{orivec}{\let\if@custvec\iffalse} +\let\if@envcntsame\iffalse +\DeclareOption{envcountsame}{\let\if@envcntsame\iftrue} +\let\if@envcntsect\iffalse +\DeclareOption{envcountsect}{\let\if@envcntsect\iftrue} +\let\if@runhead\iffalse +\DeclareOption{runningheads}{\let\if@runhead\iftrue} + +\let\if@openright\iftrue +\let\if@openbib\iffalse +\DeclareOption{openbib}{\let\if@openbib\iftrue} + +% languages +\let\switcht@@therlang\relax +\def\ds@deutsch{\def\switcht@@therlang{\switcht@deutsch}} +\def\ds@francais{\def\switcht@@therlang{\switcht@francais}} + +\DeclareOption*{\PassOptionsToClass{\CurrentOption}{article}} + +\ProcessOptions + +\LoadClass[twoside]{article} +\RequirePackage{multicol} % needed for the list of participants, index +\RequirePackage{aliascnt} + +\setlength{\textwidth}{12.2cm} +\setlength{\textheight}{19.3cm} +\renewcommand\@pnumwidth{2em} +\renewcommand\@tocrmarg{3.5em} +% +\def\@dottedtocline#1#2#3#4#5{% + \ifnum #1>\c@tocdepth \else + \vskip \z@ \@plus.2\p@ + {\leftskip #2\relax \rightskip \@tocrmarg \advance\rightskip by 0pt plus 2cm + \parfillskip -\rightskip \pretolerance=10000 + \parindent #2\relax\@afterindenttrue + \interlinepenalty\@M + \leavevmode + \@tempdima #3\relax + \advance\leftskip \@tempdima \null\nobreak\hskip -\leftskip + {#4}\nobreak + \leaders\hbox{$\m@th + \mkern \@dotsep mu\hbox{.}\mkern \@dotsep + mu$}\hfill + \nobreak + \hb@xt@\@pnumwidth{\hfil\normalfont \normalcolor #5}% + \par}% + \fi} +% +\def\switcht@albion{% +\def\abstractname{Abstract.} +\def\ackname{Acknowledgement.} +\def\andname{and} +\def\lastandname{\unskip, and} +\def\appendixname{Appendix} +\def\chaptername{Chapter} +\def\claimname{Claim} +\def\conjecturename{Conjecture} +\def\contentsname{Table of Contents} +\def\corollaryname{Corollary} +\def\definitionname{Definition} +\def\examplename{Example} +\def\exercisename{Exercise} +\def\figurename{Fig.} +\def\keywordname{{\bf Keywords:}} +\def\indexname{Index} +\def\lemmaname{Lemma} +\def\contriblistname{List of Contributors} +\def\listfigurename{List of Figures} +\def\listtablename{List of Tables} +\def\mailname{{\it Correspondence to\/}:} +\def\noteaddname{Note added in proof} +\def\notename{Note} +\def\partname{Part} +\def\problemname{Problem} +\def\proofname{Proof} +\def\propertyname{Property} +\def\propositionname{Proposition} +\def\questionname{Question} +\def\remarkname{Remark} +\def\seename{see} +\def\solutionname{Solution} +\def\subclassname{{\it Subject Classifications\/}:} +\def\tablename{Table} +\def\theoremname{Theorem}} +\switcht@albion +% Names of theorem like environments are already defined +% but must be translated if another language is chosen +% +% French section +\def\switcht@francais{%\typeout{On parle francais.}% + \def\abstractname{R\'esum\'e.}% + \def\ackname{Remerciements.}% + \def\andname{et}% + \def\lastandname{ et}% + \def\appendixname{Appendice} + \def\chaptername{Chapitre}% + \def\claimname{Pr\'etention}% + \def\conjecturename{Hypoth\`ese}% + \def\contentsname{Table des mati\`eres}% + \def\corollaryname{Corollaire}% + \def\definitionname{D\'efinition}% + \def\examplename{Exemple}% + \def\exercisename{Exercice}% + \def\figurename{Fig.}% + \def\keywordname{{\bf Mots-cl\'e:}} + \def\indexname{Index} + \def\lemmaname{Lemme}% + \def\contriblistname{Liste des contributeurs} + \def\listfigurename{Liste des figures}% + \def\listtablename{Liste des tables}% + \def\mailname{{\it Correspondence to\/}:} + \def\noteaddname{Note ajout\'ee \`a l'\'epreuve}% + \def\notename{Remarque}% + \def\partname{Partie}% + \def\problemname{Probl\`eme}% + \def\proofname{Preuve}% + \def\propertyname{Caract\'eristique}% +%\def\propositionname{Proposition}% + \def\questionname{Question}% + \def\remarkname{Remarque}% + \def\seename{voir} + \def\solutionname{Solution}% + \def\subclassname{{\it Subject Classifications\/}:} + \def\tablename{Tableau}% + \def\theoremname{Th\'eor\`eme}% +} +% +% German section +\def\switcht@deutsch{%\typeout{Man spricht deutsch.}% + \def\abstractname{Zusammenfassung.}% + \def\ackname{Danksagung.}% + \def\andname{und}% + \def\lastandname{ und}% + \def\appendixname{Anhang}% + \def\chaptername{Kapitel}% + \def\claimname{Behauptung}% + \def\conjecturename{Hypothese}% + \def\contentsname{Inhaltsverzeichnis}% + \def\corollaryname{Korollar}% +%\def\definitionname{Definition}% + \def\examplename{Beispiel}% + \def\exercisename{\"Ubung}% + \def\figurename{Abb.}% + \def\keywordname{{\bf Schl\"usselw\"orter:}} + \def\indexname{Index} +%\def\lemmaname{Lemma}% + \def\contriblistname{Mitarbeiter} + \def\listfigurename{Abbildungsverzeichnis}% + \def\listtablename{Tabellenverzeichnis}% + \def\mailname{{\it Correspondence to\/}:} + \def\noteaddname{Nachtrag}% + \def\notename{Anmerkung}% + \def\partname{Teil}% +%\def\problemname{Problem}% + \def\proofname{Beweis}% + \def\propertyname{Eigenschaft}% +%\def\propositionname{Proposition}% + \def\questionname{Frage}% + \def\remarkname{Anmerkung}% + \def\seename{siehe} + \def\solutionname{L\"osung}% + \def\subclassname{{\it Subject Classifications\/}:} + \def\tablename{Tabelle}% +%\def\theoremname{Theorem}% +} + +% Ragged bottom for the actual page +\def\thisbottomragged{\def\@textbottom{\vskip\z@ plus.0001fil +\global\let\@textbottom\relax}} + +\renewcommand\small{% + \@setfontsize\small\@ixpt{11}% + \abovedisplayskip 8.5\p@ \@plus3\p@ \@minus4\p@ + \abovedisplayshortskip \z@ \@plus2\p@ + \belowdisplayshortskip 4\p@ \@plus2\p@ \@minus2\p@ + \def\@listi{\leftmargin\leftmargini + \parsep 0\p@ \@plus1\p@ \@minus\p@ + \topsep 8\p@ \@plus2\p@ \@minus4\p@ + \itemsep0\p@}% + \belowdisplayskip \abovedisplayskip +} + +\frenchspacing +\widowpenalty=10000 +\clubpenalty=10000 + +\setlength\oddsidemargin {63\p@} +\setlength\evensidemargin {63\p@} +\setlength\marginparwidth {90\p@} + +\setlength\headsep {16\p@} + +\setlength\footnotesep{7.7\p@} +\setlength\textfloatsep{8mm\@plus 2\p@ \@minus 4\p@} +\setlength\intextsep {8mm\@plus 2\p@ \@minus 2\p@} + +\setcounter{secnumdepth}{2} + +\newcounter {chapter} +\renewcommand\thechapter {\@arabic\c@chapter} + +\newif\if@mainmatter \@mainmattertrue +\newcommand\frontmatter{\cleardoublepage + \@mainmatterfalse\pagenumbering{Roman}} +\newcommand\mainmatter{\cleardoublepage + \@mainmattertrue\pagenumbering{arabic}} +\newcommand\backmatter{\if@openright\cleardoublepage\else\clearpage\fi + \@mainmatterfalse} + +\renewcommand\part{\cleardoublepage + \thispagestyle{empty}% + \if@twocolumn + \onecolumn + \@tempswatrue + \else + \@tempswafalse + \fi + \null\vfil + \secdef\@part\@spart} + +\def\@part[#1]#2{% + \ifnum \c@secnumdepth >-2\relax + \refstepcounter{part}% + \addcontentsline{toc}{part}{\thepart\hspace{1em}#1}% + \else + \addcontentsline{toc}{part}{#1}% + \fi + \markboth{}{}% + {\centering + \interlinepenalty \@M + \normalfont + \ifnum \c@secnumdepth >-2\relax + \huge\bfseries \partname~\thepart + \par + \vskip 20\p@ + \fi + \Huge \bfseries #2\par}% + \@endpart} +\def\@spart#1{% + {\centering + \interlinepenalty \@M + \normalfont + \Huge \bfseries #1\par}% + \@endpart} +\def\@endpart{\vfil\newpage + \if@twoside + \null + \thispagestyle{empty}% + \newpage + \fi + \if@tempswa + \twocolumn + \fi} + +\newcommand\chapter{\clearpage + \thispagestyle{empty}% + \global\@topnum\z@ + \@afterindentfalse + \secdef\@chapter\@schapter} +\def\@chapter[#1]#2{\ifnum \c@secnumdepth >\m@ne + \if@mainmatter + \refstepcounter{chapter}% + \typeout{\@chapapp\space\thechapter.}% + \addcontentsline{toc}{chapter}% + {\protect\numberline{\thechapter}#1}% + \else + \addcontentsline{toc}{chapter}{#1}% + \fi + \else + \addcontentsline{toc}{chapter}{#1}% + \fi + \chaptermark{#1}% + \addtocontents{lof}{\protect\addvspace{10\p@}}% + \addtocontents{lot}{\protect\addvspace{10\p@}}% + \if@twocolumn + \@topnewpage[\@makechapterhead{#2}]% + \else + \@makechapterhead{#2}% + \@afterheading + \fi} +\def\@makechapterhead#1{% +% \vspace*{50\p@}% + {\centering + \ifnum \c@secnumdepth >\m@ne + \if@mainmatter + \large\bfseries \@chapapp{} \thechapter + \par\nobreak + \vskip 20\p@ + \fi + \fi + \interlinepenalty\@M + \Large \bfseries #1\par\nobreak + \vskip 40\p@ + }} +\def\@schapter#1{\if@twocolumn + \@topnewpage[\@makeschapterhead{#1}]% + \else + \@makeschapterhead{#1}% + \@afterheading + \fi} +\def\@makeschapterhead#1{% +% \vspace*{50\p@}% + {\centering + \normalfont + \interlinepenalty\@M + \Large \bfseries #1\par\nobreak + \vskip 40\p@ + }} + +\renewcommand\section{\@startsection{section}{1}{\z@}% + {-18\p@ \@plus -4\p@ \@minus -4\p@}% + {12\p@ \@plus 4\p@ \@minus 4\p@}% + {\normalfont\large\bfseries\boldmath + \rightskip=\z@ \@plus 8em\pretolerance=10000 }} +\renewcommand\subsection{\@startsection{subsection}{2}{\z@}% + {-18\p@ \@plus -4\p@ \@minus -4\p@}% + {8\p@ \@plus 4\p@ \@minus 4\p@}% + {\normalfont\normalsize\bfseries\boldmath + \rightskip=\z@ \@plus 8em\pretolerance=10000 }} +\renewcommand\subsubsection{\@startsection{subsubsection}{3}{\z@}% + {-18\p@ \@plus -4\p@ \@minus -4\p@}% + {-0.5em \@plus -0.22em \@minus -0.1em}% + {\normalfont\normalsize\bfseries\boldmath}} +\renewcommand\paragraph{\@startsection{paragraph}{4}{\z@}% + {-12\p@ \@plus -4\p@ \@minus -4\p@}% + {-0.5em \@plus -0.22em \@minus -0.1em}% + {\normalfont\normalsize\itshape}} +\renewcommand\subparagraph[1]{\typeout{LLNCS warning: You should not use + \string\subparagraph\space with this class}\vskip0.5cm +You should not use \verb|\subparagraph| with this class.\vskip0.5cm} + +\DeclareMathSymbol{\Gamma}{\mathalpha}{letters}{"00} +\DeclareMathSymbol{\Delta}{\mathalpha}{letters}{"01} +\DeclareMathSymbol{\Theta}{\mathalpha}{letters}{"02} +\DeclareMathSymbol{\Lambda}{\mathalpha}{letters}{"03} +\DeclareMathSymbol{\Xi}{\mathalpha}{letters}{"04} +\DeclareMathSymbol{\Pi}{\mathalpha}{letters}{"05} +\DeclareMathSymbol{\Sigma}{\mathalpha}{letters}{"06} +\DeclareMathSymbol{\Upsilon}{\mathalpha}{letters}{"07} +\DeclareMathSymbol{\Phi}{\mathalpha}{letters}{"08} +\DeclareMathSymbol{\Psi}{\mathalpha}{letters}{"09} +\DeclareMathSymbol{\Omega}{\mathalpha}{letters}{"0A} + +\let\footnotesize\small + +\if@custvec +\def\vec#1{\mathchoice{\mbox{\boldmath$\displaystyle#1$}} +{\mbox{\boldmath$\textstyle#1$}} +{\mbox{\boldmath$\scriptstyle#1$}} +{\mbox{\boldmath$\scriptscriptstyle#1$}}} +\fi + +\def\squareforqed{\hbox{\rlap{$\sqcap$}$\sqcup$}} +\def\qed{\ifmmode\squareforqed\else{\unskip\nobreak\hfil +\penalty50\hskip1em\null\nobreak\hfil\squareforqed +\parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi} + +\def\getsto{\mathrel{\mathchoice {\vcenter{\offinterlineskip +\halign{\hfil +$\displaystyle##$\hfil\cr\gets\cr\to\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr\gets +\cr\to\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr\gets +\cr\to\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr +\gets\cr\to\cr}}}}} +\def\lid{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil +$\displaystyle##$\hfil\cr<\cr\noalign{\vskip1.2pt}=\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr<\cr +\noalign{\vskip1.2pt}=\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr<\cr +\noalign{\vskip1pt}=\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr +<\cr +\noalign{\vskip0.9pt}=\cr}}}}} +\def\gid{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil +$\displaystyle##$\hfil\cr>\cr\noalign{\vskip1.2pt}=\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr>\cr +\noalign{\vskip1.2pt}=\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr>\cr +\noalign{\vskip1pt}=\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr +>\cr +\noalign{\vskip0.9pt}=\cr}}}}} +\def\grole{\mathrel{\mathchoice {\vcenter{\offinterlineskip +\halign{\hfil +$\displaystyle##$\hfil\cr>\cr\noalign{\vskip-1pt}<\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr +>\cr\noalign{\vskip-1pt}<\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr +>\cr\noalign{\vskip-0.8pt}<\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr +>\cr\noalign{\vskip-0.3pt}<\cr}}}}} +\def\bbbr{{\rm I\!R}} %reelle Zahlen +\def\bbbm{{\rm I\!M}} +\def\bbbn{{\rm I\!N}} %natuerliche Zahlen +\def\bbbf{{\rm I\!F}} +\def\bbbh{{\rm I\!H}} +\def\bbbk{{\rm I\!K}} +\def\bbbp{{\rm I\!P}} +\def\bbbone{{\mathchoice {\rm 1\mskip-4mu l} {\rm 1\mskip-4mu l} +{\rm 1\mskip-4.5mu l} {\rm 1\mskip-5mu l}}} +\def\bbbc{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm C$}\hbox{\hbox +to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}} +{\setbox0=\hbox{$\textstyle\rm C$}\hbox{\hbox +to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptstyle\rm C$}\hbox{\hbox +to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptscriptstyle\rm C$}\hbox{\hbox +to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}}}} +\def\bbbq{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm +Q$}\hbox{\raise +0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.8\ht0\hss}\box0}} +{\setbox0=\hbox{$\textstyle\rm Q$}\hbox{\raise +0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.8\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptstyle\rm Q$}\hbox{\raise +0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.7\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptscriptstyle\rm Q$}\hbox{\raise +0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.7\ht0\hss}\box0}}}} +\def\bbbt{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm +T$}\hbox{\hbox to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}} +{\setbox0=\hbox{$\textstyle\rm T$}\hbox{\hbox +to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptstyle\rm T$}\hbox{\hbox +to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptscriptstyle\rm T$}\hbox{\hbox +to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}}}} +\def\bbbs{{\mathchoice +{\setbox0=\hbox{$\displaystyle \rm S$}\hbox{\raise0.5\ht0\hbox +to0pt{\kern0.35\wd0\vrule height0.45\ht0\hss}\hbox +to0pt{\kern0.55\wd0\vrule height0.5\ht0\hss}\box0}} +{\setbox0=\hbox{$\textstyle \rm S$}\hbox{\raise0.5\ht0\hbox +to0pt{\kern0.35\wd0\vrule height0.45\ht0\hss}\hbox +to0pt{\kern0.55\wd0\vrule height0.5\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptstyle \rm S$}\hbox{\raise0.5\ht0\hbox +to0pt{\kern0.35\wd0\vrule height0.45\ht0\hss}\raise0.05\ht0\hbox +to0pt{\kern0.5\wd0\vrule height0.45\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptscriptstyle\rm S$}\hbox{\raise0.5\ht0\hbox +to0pt{\kern0.4\wd0\vrule height0.45\ht0\hss}\raise0.05\ht0\hbox +to0pt{\kern0.55\wd0\vrule height0.45\ht0\hss}\box0}}}} +\def\bbbz{{\mathchoice {\hbox{$\mathsf\textstyle Z\kern-0.4em Z$}} +{\hbox{$\mathsf\textstyle Z\kern-0.4em Z$}} +{\hbox{$\mathsf\scriptstyle Z\kern-0.3em Z$}} +{\hbox{$\mathsf\scriptscriptstyle Z\kern-0.2em Z$}}}} + +\let\ts\, + +\setlength\leftmargini {17\p@} +\setlength\leftmargin {\leftmargini} +\setlength\leftmarginii {\leftmargini} +\setlength\leftmarginiii {\leftmargini} +\setlength\leftmarginiv {\leftmargini} +\setlength \labelsep {.5em} +\setlength \labelwidth{\leftmargini} +\addtolength\labelwidth{-\labelsep} + +\def\@listI{\leftmargin\leftmargini + \parsep 0\p@ \@plus1\p@ \@minus\p@ + \topsep 8\p@ \@plus2\p@ \@minus4\p@ + \itemsep0\p@} +\let\@listi\@listI +\@listi +\def\@listii {\leftmargin\leftmarginii + \labelwidth\leftmarginii + \advance\labelwidth-\labelsep + \topsep 0\p@ \@plus2\p@ \@minus\p@} +\def\@listiii{\leftmargin\leftmarginiii + \labelwidth\leftmarginiii + \advance\labelwidth-\labelsep + \topsep 0\p@ \@plus\p@\@minus\p@ + \parsep \z@ + \partopsep \p@ \@plus\z@ \@minus\p@} + +\renewcommand\labelitemi{\normalfont\bfseries --} +\renewcommand\labelitemii{$\m@th\bullet$} + +\setlength\arraycolsep{1.4\p@} +\setlength\tabcolsep{1.4\p@} + +\def\tableofcontents{\chapter*{\contentsname\@mkboth{{\contentsname}}% + {{\contentsname}}} + \def\authcount##1{\setcounter{auco}{##1}\setcounter{@auth}{1}} + \def\lastand{\ifnum\value{auco}=2\relax + \unskip{} \andname\ + \else + \unskip \lastandname\ + \fi}% + \def\and{\stepcounter{@auth}\relax + \ifnum\value{@auth}=\value{auco}% + \lastand + \else + \unskip, + \fi}% + \@starttoc{toc}\if@restonecol\twocolumn\fi} + +\def\l@part#1#2{\addpenalty{\@secpenalty}% + \addvspace{2em plus\p@}% % space above part line + \begingroup + \parindent \z@ + \rightskip \z@ plus 5em + \hrule\vskip5pt + \large % same size as for a contribution heading + \bfseries\boldmath % set line in boldface + \leavevmode % TeX command to enter horizontal mode. + #1\par + \vskip5pt + \hrule + \vskip1pt + \nobreak % Never break after part entry + \endgroup} + +\def\@dotsep{2} + +\let\phantomsection=\relax + +\def\hyperhrefextend{\ifx\hyper@anchor\@undefined\else +{}\fi} + +\def\addnumcontentsmark#1#2#3{% +\addtocontents{#1}{\protect\contentsline{#2}{\protect\numberline + {\thechapter}#3}{\thepage}\hyperhrefextend}}% +\def\addcontentsmark#1#2#3{% +\addtocontents{#1}{\protect\contentsline{#2}{#3}{\thepage}\hyperhrefextend}}% +\def\addcontentsmarkwop#1#2#3{% +\addtocontents{#1}{\protect\contentsline{#2}{#3}{0}\hyperhrefextend}}% + +\def\@adcmk[#1]{\ifcase #1 \or +\def\@gtempa{\addnumcontentsmark}% + \or \def\@gtempa{\addcontentsmark}% + \or \def\@gtempa{\addcontentsmarkwop}% + \fi\@gtempa{toc}{chapter}% +} +\def\addtocmark{% +\phantomsection +\@ifnextchar[{\@adcmk}{\@adcmk[3]}% +} + +\def\l@chapter#1#2{\addpenalty{-\@highpenalty} + \vskip 1.0em plus 1pt \@tempdima 1.5em \begingroup + \parindent \z@ \rightskip \@tocrmarg + \advance\rightskip by 0pt plus 2cm + \parfillskip -\rightskip \pretolerance=10000 + \leavevmode \advance\leftskip\@tempdima \hskip -\leftskip + {\large\bfseries\boldmath#1}\ifx0#2\hfil\null + \else + \nobreak + \leaders\hbox{$\m@th \mkern \@dotsep mu.\mkern + \@dotsep mu$}\hfill + \nobreak\hbox to\@pnumwidth{\hss #2}% + \fi\par + \penalty\@highpenalty \endgroup} + +\def\l@title#1#2{\addpenalty{-\@highpenalty} + \addvspace{8pt plus 1pt} + \@tempdima \z@ + \begingroup + \parindent \z@ \rightskip \@tocrmarg + \advance\rightskip by 0pt plus 2cm + \parfillskip -\rightskip \pretolerance=10000 + \leavevmode \advance\leftskip\@tempdima \hskip -\leftskip + #1\nobreak + \leaders\hbox{$\m@th \mkern \@dotsep mu.\mkern + \@dotsep mu$}\hfill + \nobreak\hbox to\@pnumwidth{\hss #2}\par + \penalty\@highpenalty \endgroup} + +\def\l@author#1#2{\addpenalty{\@highpenalty} + \@tempdima=15\p@ %\z@ + \begingroup + \parindent \z@ \rightskip \@tocrmarg + \advance\rightskip by 0pt plus 2cm + \pretolerance=10000 + \leavevmode \advance\leftskip\@tempdima %\hskip -\leftskip + \textit{#1}\par + \penalty\@highpenalty \endgroup} + +\setcounter{tocdepth}{0} +\newdimen\tocchpnum +\newdimen\tocsecnum +\newdimen\tocsectotal +\newdimen\tocsubsecnum +\newdimen\tocsubsectotal +\newdimen\tocsubsubsecnum +\newdimen\tocsubsubsectotal +\newdimen\tocparanum +\newdimen\tocparatotal +\newdimen\tocsubparanum +\tocchpnum=\z@ % no chapter numbers +\tocsecnum=15\p@ % section 88. plus 2.222pt +\tocsubsecnum=23\p@ % subsection 88.8 plus 2.222pt +\tocsubsubsecnum=27\p@ % subsubsection 88.8.8 plus 1.444pt +\tocparanum=35\p@ % paragraph 88.8.8.8 plus 1.666pt +\tocsubparanum=43\p@ % subparagraph 88.8.8.8.8 plus 1.888pt +\def\calctocindent{% +\tocsectotal=\tocchpnum +\advance\tocsectotal by\tocsecnum +\tocsubsectotal=\tocsectotal +\advance\tocsubsectotal by\tocsubsecnum +\tocsubsubsectotal=\tocsubsectotal +\advance\tocsubsubsectotal by\tocsubsubsecnum +\tocparatotal=\tocsubsubsectotal +\advance\tocparatotal by\tocparanum} +\calctocindent + +\def\l@section{\@dottedtocline{1}{\tocchpnum}{\tocsecnum}} +\def\l@subsection{\@dottedtocline{2}{\tocsectotal}{\tocsubsecnum}} +\def\l@subsubsection{\@dottedtocline{3}{\tocsubsectotal}{\tocsubsubsecnum}} +\def\l@paragraph{\@dottedtocline{4}{\tocsubsubsectotal}{\tocparanum}} +\def\l@subparagraph{\@dottedtocline{5}{\tocparatotal}{\tocsubparanum}} + +\def\listoffigures{\@restonecolfalse\if@twocolumn\@restonecoltrue\onecolumn + \fi\section*{\listfigurename\@mkboth{{\listfigurename}}{{\listfigurename}}} + \@starttoc{lof}\if@restonecol\twocolumn\fi} +\def\l@figure{\@dottedtocline{1}{0em}{1.5em}} + +\def\listoftables{\@restonecolfalse\if@twocolumn\@restonecoltrue\onecolumn + \fi\section*{\listtablename\@mkboth{{\listtablename}}{{\listtablename}}} + \@starttoc{lot}\if@restonecol\twocolumn\fi} +\let\l@table\l@figure + +\renewcommand\listoffigures{% + \section*{\listfigurename + \@mkboth{\listfigurename}{\listfigurename}}% + \@starttoc{lof}% + } + +\renewcommand\listoftables{% + \section*{\listtablename + \@mkboth{\listtablename}{\listtablename}}% + \@starttoc{lot}% + } + +\ifx\oribibl\undefined +\ifx\citeauthoryear\undefined +\renewenvironment{thebibliography}[1] + {\section*{\refname} + \def\@biblabel##1{##1.} + \small + \list{\@biblabel{\@arabic\c@enumiv}}% + {\settowidth\labelwidth{\@biblabel{#1}}% + \leftmargin\labelwidth + \advance\leftmargin\labelsep + \if@openbib + \advance\leftmargin\bibindent + \itemindent -\bibindent + \listparindent \itemindent + \parsep \z@ + \fi + \usecounter{enumiv}% + \let\p@enumiv\@empty + \renewcommand\theenumiv{\@arabic\c@enumiv}}% + \if@openbib + \renewcommand\newblock{\par}% + \else + \renewcommand\newblock{\hskip .11em \@plus.33em \@minus.07em}% + \fi + \sloppy\clubpenalty4000\widowpenalty4000% + \sfcode`\.=\@m} + {\def\@noitemerr + {\@latex@warning{Empty `thebibliography' environment}}% + \endlist} +\def\@lbibitem[#1]#2{\item[{[#1]}\hfill]\if@filesw + {\let\protect\noexpand\immediate + \write\@auxout{\string\bibcite{#2}{#1}}}\fi\ignorespaces} +\newcount\@tempcntc +\def\@citex[#1]#2{\if@filesw\immediate\write\@auxout{\string\citation{#2}}\fi + \@tempcnta\z@\@tempcntb\m@ne\def\@citea{}\@cite{\@for\@citeb:=#2\do + {\@ifundefined + {b@\@citeb}{\@citeo\@tempcntb\m@ne\@citea\def\@citea{,}{\bfseries + ?}\@warning + {Citation `\@citeb' on page \thepage \space undefined}}% + {\setbox\z@\hbox{\global\@tempcntc0\csname b@\@citeb\endcsname\relax}% + \ifnum\@tempcntc=\z@ \@citeo\@tempcntb\m@ne + \@citea\def\@citea{,}\hbox{\csname b@\@citeb\endcsname}% + \else + \advance\@tempcntb\@ne + \ifnum\@tempcntb=\@tempcntc + \else\advance\@tempcntb\m@ne\@citeo + \@tempcnta\@tempcntc\@tempcntb\@tempcntc\fi\fi}}\@citeo}{#1}} +\def\@citeo{\ifnum\@tempcnta>\@tempcntb\else + \@citea\def\@citea{,\,\hskip\z@skip}% + \ifnum\@tempcnta=\@tempcntb\the\@tempcnta\else + {\advance\@tempcnta\@ne\ifnum\@tempcnta=\@tempcntb \else + \def\@citea{--}\fi + \advance\@tempcnta\m@ne\the\@tempcnta\@citea\the\@tempcntb}\fi\fi} +\else +\renewenvironment{thebibliography}[1] + {\section*{\refname} + \small + \list{}% + {\settowidth\labelwidth{}% + \leftmargin\parindent + \itemindent=-\parindent + \labelsep=\z@ + \if@openbib + \advance\leftmargin\bibindent + \itemindent -\bibindent + \listparindent \itemindent + \parsep \z@ + \fi + \usecounter{enumiv}% + \let\p@enumiv\@empty + \renewcommand\theenumiv{}}% + \if@openbib + \renewcommand\newblock{\par}% + \else + \renewcommand\newblock{\hskip .11em \@plus.33em \@minus.07em}% + \fi + \sloppy\clubpenalty4000\widowpenalty4000% + \sfcode`\.=\@m} + {\def\@noitemerr + {\@latex@warning{Empty `thebibliography' environment}}% + \endlist} + \def\@cite#1{#1}% + \def\@lbibitem[#1]#2{\item[]\if@filesw + {\def\protect##1{\string ##1\space}\immediate + \write\@auxout{\string\bibcite{#2}{#1}}}\fi\ignorespaces} + \fi +\else +\@cons\@openbib@code{\noexpand\small} +\fi + +\def\idxquad{\hskip 10\p@}% space that divides entry from number + +\def\@idxitem{\par\hangindent 10\p@} + +\def\subitem{\par\setbox0=\hbox{--\enspace}% second order + \noindent\hangindent\wd0\box0}% index entry + +\def\subsubitem{\par\setbox0=\hbox{--\,--\enspace}% third + \noindent\hangindent\wd0\box0}% order index entry + +\def\indexspace{\par \vskip 10\p@ plus5\p@ minus3\p@\relax} + +\renewenvironment{theindex} + {\@mkboth{\indexname}{\indexname}% + \thispagestyle{empty}\parindent\z@ + \parskip\z@ \@plus .3\p@\relax + \let\item\par + \def\,{\relax\ifmmode\mskip\thinmuskip + \else\hskip0.2em\ignorespaces\fi}% + \normalfont\small + \begin{multicols}{2}[\@makeschapterhead{\indexname}]% + } + {\end{multicols}} + +\renewcommand\footnoterule{% + \kern-3\p@ + \hrule\@width 2truecm + \kern2.6\p@} + \newdimen\fnindent + \fnindent1em +\long\def\@makefntext#1{% + \parindent \fnindent% + \leftskip \fnindent% + \noindent + \llap{\hb@xt@1em{\hss\@makefnmark\ }}\ignorespaces#1} + +\long\def\@makecaption#1#2{% + \small + \vskip\abovecaptionskip + \sbox\@tempboxa{{\bfseries #1.} #2}% + \ifdim \wd\@tempboxa >\hsize + {\bfseries #1.} #2\par + \else + \global \@minipagefalse + \hb@xt@\hsize{\hfil\box\@tempboxa\hfil}% + \fi + \vskip\belowcaptionskip} + +\def\fps@figure{htbp} +\def\fnum@figure{\figurename\thinspace\thefigure} +\def \@floatboxreset {% + \reset@font + \small + \@setnobreak + \@setminipage +} +\def\fps@table{htbp} +\def\fnum@table{\tablename~\thetable} +\renewenvironment{table} + {\setlength\abovecaptionskip{0\p@}% + \setlength\belowcaptionskip{10\p@}% + \@float{table}} + {\end@float} +\renewenvironment{table*} + {\setlength\abovecaptionskip{0\p@}% + \setlength\belowcaptionskip{10\p@}% + \@dblfloat{table}} + {\end@dblfloat} + +\long\def\@caption#1[#2]#3{\par\addcontentsline{\csname + ext@#1\endcsname}{#1}{\protect\numberline{\csname + the#1\endcsname}{\ignorespaces #2}}\begingroup + \@parboxrestore + \@makecaption{\csname fnum@#1\endcsname}{\ignorespaces #3}\par + \endgroup} + +% LaTeX does not provide a command to enter the authors institute +% addresses. The \institute command is defined here. + +\newcounter{@inst} +\newcounter{@auth} +\newcounter{auco} +\newdimen\instindent +\newbox\authrun +\newtoks\authorrunning +\newtoks\tocauthor +\newbox\titrun +\newtoks\titlerunning +\newtoks\toctitle + +\def\clearheadinfo{\gdef\@author{No Author Given}% + \gdef\@title{No Title Given}% + \gdef\@subtitle{}% + \gdef\@institute{No Institute Given}% + \gdef\@thanks{}% + \global\titlerunning={}\global\authorrunning={}% + \global\toctitle={}\global\tocauthor={}} + +\def\institute#1{\gdef\@institute{#1}} + +\def\institutename{\par + \begingroup + \parskip=\z@ + \parindent=\z@ + \setcounter{@inst}{1}% + \def\and{\par\stepcounter{@inst}% + \noindent$^{\the@inst}$\enspace\ignorespaces}% + \setbox0=\vbox{\def\thanks##1{}\@institute}% + \ifnum\c@@inst=1\relax + \gdef\fnnstart{0}% + \else + \xdef\fnnstart{\c@@inst}% + \setcounter{@inst}{1}% + \noindent$^{\the@inst}$\enspace + \fi + \ignorespaces + \@institute\par + \endgroup} + +\def\@fnsymbol#1{\ensuremath{\ifcase#1\or\star\or{\star\star}\or + {\star\star\star}\or \dagger\or \ddagger\or + \mathchar "278\or \mathchar "27B\or \|\or **\or \dagger\dagger + \or \ddagger\ddagger \else\@ctrerr\fi}} + +\def\inst#1{\unskip$^{#1}$} +\def\fnmsep{\unskip$^,$} +\def\email#1{{\tt#1}} +\AtBeginDocument{\@ifundefined{url}{\def\url#1{#1}}{}% +\@ifpackageloaded{babel}{% +\@ifundefined{extrasenglish}{}{\addto\extrasenglish{\switcht@albion}}% +\@ifundefined{extrasfrenchb}{}{\addto\extrasfrenchb{\switcht@francais}}% +\@ifundefined{extrasgerman}{}{\addto\extrasgerman{\switcht@deutsch}}% +}{\switcht@@therlang}% +\providecommand{\keywords}[1]{\par\addvspace\baselineskip +\noindent\keywordname\enspace\ignorespaces#1}% +} +\def\homedir{\~{ }} + +\def\subtitle#1{\gdef\@subtitle{#1}} +\clearheadinfo +% +%%% to avoid hyperref warnings +\providecommand*{\toclevel@author}{999} +%%% to make title-entry parent of section-entries +\providecommand*{\toclevel@title}{0} +% +\renewcommand\maketitle{\newpage +\phantomsection + \refstepcounter{chapter}% + \stepcounter{section}% + \setcounter{section}{0}% + \setcounter{subsection}{0}% + \setcounter{figure}{0} + \setcounter{table}{0} + \setcounter{equation}{0} + \setcounter{footnote}{0}% + \begingroup + \parindent=\z@ + \renewcommand\thefootnote{\@fnsymbol\c@footnote}% + \if@twocolumn + \ifnum \col@number=\@ne + \@maketitle + \else + \twocolumn[\@maketitle]% + \fi + \else + \newpage + \global\@topnum\z@ % Prevents figures from going at top of page. + \@maketitle + \fi + \thispagestyle{empty}\@thanks +% + \def\\{\unskip\ \ignorespaces}\def\inst##1{\unskip{}}% + \def\thanks##1{\unskip{}}\def\fnmsep{\unskip}% + \instindent=\hsize + \advance\instindent by-\headlineindent + \if!\the\toctitle!\addcontentsline{toc}{title}{\@title}\else + \addcontentsline{toc}{title}{\the\toctitle}\fi + \if@runhead + \if!\the\titlerunning!\else + \edef\@title{\the\titlerunning}% + \fi + \global\setbox\titrun=\hbox{\small\rm\unboldmath\ignorespaces\@title}% + \ifdim\wd\titrun>\instindent + \typeout{Title too long for running head. Please supply}% + \typeout{a shorter form with \string\titlerunning\space prior to + \string\maketitle}% + \global\setbox\titrun=\hbox{\small\rm + Title Suppressed Due to Excessive Length}% + \fi + \xdef\@title{\copy\titrun}% + \fi +% + \if!\the\tocauthor!\relax + {\def\and{\noexpand\protect\noexpand\and}% + \protected@xdef\toc@uthor{\@author}}% + \else + \def\\{\noexpand\protect\noexpand\newline}% + \protected@xdef\scratch{\the\tocauthor}% + \protected@xdef\toc@uthor{\scratch}% + \fi + \addtocontents{toc}{\noexpand\protect\noexpand\authcount{\the\c@auco}}% + \addcontentsline{toc}{author}{\toc@uthor}% + \if@runhead + \if!\the\authorrunning! + \value{@inst}=\value{@auth}% + \setcounter{@auth}{1}% + \else + \edef\@author{\the\authorrunning}% + \fi + \global\setbox\authrun=\hbox{\small\unboldmath\@author\unskip}% + \ifdim\wd\authrun>\instindent + \typeout{Names of authors too long for running head. Please supply}% + \typeout{a shorter form with \string\authorrunning\space prior to + \string\maketitle}% + \global\setbox\authrun=\hbox{\small\rm + Authors Suppressed Due to Excessive Length}% + \fi + \xdef\@author{\copy\authrun}% + \markboth{\@author}{\@title}% + \fi + \endgroup + \setcounter{footnote}{\fnnstart}% + \clearheadinfo} +% +\def\@maketitle{\newpage + \markboth{}{}% + \def\lastand{\ifnum\value{@inst}=2\relax + \unskip{} \andname\ + \else + \unskip \lastandname\ + \fi}% + \def\and{\stepcounter{@auth}\relax + \ifnum\value{@auth}=\value{@inst}% + \lastand + \else + \unskip, + \fi}% + \begin{center}% + \let\newline\\ + {\Large \bfseries\boldmath + \pretolerance=10000 + \@title \par}\vskip .8cm +\if!\@subtitle!\else {\large \bfseries\boldmath + \vskip -.65cm + \pretolerance=10000 + \@subtitle \par}\vskip .8cm\fi + \setbox0=\vbox{\setcounter{@auth}{1}\def\and{\stepcounter{@auth}}% + \def\thanks##1{}\@author}% + \global\value{@inst}=\value{@auth}% + \global\value{auco}=\value{@auth}% + \setcounter{@auth}{1}% +{\lineskip .5em +\noindent\ignorespaces +\@author\vskip.35cm} + {\small\institutename} + \end{center}% + } + +% definition of the "\spnewtheorem" command. +% +% Usage: +% +% \spnewtheorem{env_nam}{caption}[within]{cap_font}{body_font} +% or \spnewtheorem{env_nam}[numbered_like]{caption}{cap_font}{body_font} +% or \spnewtheorem*{env_nam}{caption}{cap_font}{body_font} +% +% New is "cap_font" and "body_font". It stands for +% fontdefinition of the caption and the text itself. +% +% "\spnewtheorem*" gives a theorem without number. +% +% A defined spnewthoerem environment is used as described +% by Lamport. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\def\@thmcountersep{} +\def\@thmcounterend{.} + +\def\spnewtheorem{\@ifstar{\@sthm}{\@Sthm}} + +% definition of \spnewtheorem with number + +\def\@spnthm#1#2{% + \@ifnextchar[{\@spxnthm{#1}{#2}}{\@spynthm{#1}{#2}}} +\def\@Sthm#1{\@ifnextchar[{\@spothm{#1}}{\@spnthm{#1}}} + +\def\@spxnthm#1#2[#3]#4#5{\expandafter\@ifdefinable\csname #1\endcsname + {\@definecounter{#1}\@addtoreset{#1}{#3}% + \expandafter\xdef\csname the#1\endcsname{\expandafter\noexpand + \csname the#3\endcsname \noexpand\@thmcountersep \@thmcounter{#1}}% + \expandafter\xdef\csname #1name\endcsname{#2}% + \global\@namedef{#1}{\@spthm{#1}{\csname #1name\endcsname}{#4}{#5}}% + \global\@namedef{end#1}{\@endtheorem}}} + +\def\@spynthm#1#2#3#4{\expandafter\@ifdefinable\csname #1\endcsname + {\@definecounter{#1}% + \expandafter\xdef\csname the#1\endcsname{\@thmcounter{#1}}% + \expandafter\xdef\csname #1name\endcsname{#2}% + \global\@namedef{#1}{\@spthm{#1}{\csname #1name\endcsname}{#3}{#4}}% + \global\@namedef{end#1}{\@endtheorem}}} + +\def\@spothm#1[#2]#3#4#5{% + \@ifundefined{c@#2}{\@latexerr{No theorem environment `#2' defined}\@eha}% + {\expandafter\@ifdefinable\csname #1\endcsname + {\newaliascnt{#1}{#2}% + \expandafter\xdef\csname #1name\endcsname{#3}% + \global\@namedef{#1}{\@spthm{#1}{\csname #1name\endcsname}{#4}{#5}}% + \global\@namedef{end#1}{\@endtheorem}}}} + +\def\@spthm#1#2#3#4{\topsep 7\p@ \@plus2\p@ \@minus4\p@ +\refstepcounter{#1}% +\@ifnextchar[{\@spythm{#1}{#2}{#3}{#4}}{\@spxthm{#1}{#2}{#3}{#4}}} + +\def\@spxthm#1#2#3#4{\@spbegintheorem{#2}{\csname the#1\endcsname}{#3}{#4}% + \ignorespaces} + +\def\@spythm#1#2#3#4[#5]{\@spopargbegintheorem{#2}{\csname + the#1\endcsname}{#5}{#3}{#4}\ignorespaces} + +\def\@spbegintheorem#1#2#3#4{\trivlist + \item[\hskip\labelsep{#3#1\ #2\@thmcounterend}]#4} + +\def\@spopargbegintheorem#1#2#3#4#5{\trivlist + \item[\hskip\labelsep{#4#1\ #2}]{#4(#3)\@thmcounterend\ }#5} + +% definition of \spnewtheorem* without number + +\def\@sthm#1#2{\@Ynthm{#1}{#2}} + +\def\@Ynthm#1#2#3#4{\expandafter\@ifdefinable\csname #1\endcsname + {\global\@namedef{#1}{\@Thm{\csname #1name\endcsname}{#3}{#4}}% + \expandafter\xdef\csname #1name\endcsname{#2}% + \global\@namedef{end#1}{\@endtheorem}}} + +\def\@Thm#1#2#3{\topsep 7\p@ \@plus2\p@ \@minus4\p@ +\@ifnextchar[{\@Ythm{#1}{#2}{#3}}{\@Xthm{#1}{#2}{#3}}} + +\def\@Xthm#1#2#3{\@Begintheorem{#1}{#2}{#3}\ignorespaces} + +\def\@Ythm#1#2#3[#4]{\@Opargbegintheorem{#1} + {#4}{#2}{#3}\ignorespaces} + +\def\@Begintheorem#1#2#3{#3\trivlist + \item[\hskip\labelsep{#2#1\@thmcounterend}]} + +\def\@Opargbegintheorem#1#2#3#4{#4\trivlist + \item[\hskip\labelsep{#3#1}]{#3(#2)\@thmcounterend\ }} + +\if@envcntsect + \def\@thmcountersep{.} + \spnewtheorem{theorem}{Theorem}[section]{\bfseries}{\itshape} +\else + \spnewtheorem{theorem}{Theorem}{\bfseries}{\itshape} + \if@envcntreset + \@addtoreset{theorem}{section} + \else + \@addtoreset{theorem}{chapter} + \fi +\fi + +%definition of divers theorem environments +\spnewtheorem*{claim}{Claim}{\itshape}{\rmfamily} +\spnewtheorem*{proof}{Proof}{\itshape}{\rmfamily} +\if@envcntsame % alle Umgebungen wie Theorem. + \def\spn@wtheorem#1#2#3#4{\@spothm{#1}[theorem]{#2}{#3}{#4}} +\else % alle Umgebungen mit eigenem Zaehler + \if@envcntsect % mit section numeriert + \def\spn@wtheorem#1#2#3#4{\@spxnthm{#1}{#2}[section]{#3}{#4}} + \else % nicht mit section numeriert + \if@envcntreset + \def\spn@wtheorem#1#2#3#4{\@spynthm{#1}{#2}{#3}{#4} + \@addtoreset{#1}{section}} + \else + \def\spn@wtheorem#1#2#3#4{\@spynthm{#1}{#2}{#3}{#4} + \@addtoreset{#1}{chapter}}% + \fi + \fi +\fi +\spn@wtheorem{case}{Case}{\itshape}{\rmfamily} +\spn@wtheorem{conjecture}{Conjecture}{\itshape}{\rmfamily} +\spn@wtheorem{corollary}{Corollary}{\bfseries}{\itshape} +\spn@wtheorem{definition}{Definition}{\bfseries}{\itshape} +\spn@wtheorem{example}{Example}{\itshape}{\rmfamily} +\spn@wtheorem{exercise}{Exercise}{\itshape}{\rmfamily} +\spn@wtheorem{lemma}{Lemma}{\bfseries}{\itshape} +\spn@wtheorem{note}{Note}{\itshape}{\rmfamily} +\spn@wtheorem{problem}{Problem}{\itshape}{\rmfamily} +\spn@wtheorem{property}{Property}{\itshape}{\rmfamily} +\spn@wtheorem{proposition}{Proposition}{\bfseries}{\itshape} +\spn@wtheorem{question}{Question}{\itshape}{\rmfamily} +\spn@wtheorem{solution}{Solution}{\itshape}{\rmfamily} +\spn@wtheorem{remark}{Remark}{\itshape}{\rmfamily} + +\def\@takefromreset#1#2{% + \def\@tempa{#1}% + \let\@tempd\@elt + \def\@elt##1{% + \def\@tempb{##1}% + \ifx\@tempa\@tempb\else + \@addtoreset{##1}{#2}% + \fi}% + \expandafter\expandafter\let\expandafter\@tempc\csname cl@#2\endcsname + \expandafter\def\csname cl@#2\endcsname{}% + \@tempc + \let\@elt\@tempd} + +\def\theopargself{\def\@spopargbegintheorem##1##2##3##4##5{\trivlist + \item[\hskip\labelsep{##4##1\ ##2}]{##4##3\@thmcounterend\ }##5} + \def\@Opargbegintheorem##1##2##3##4{##4\trivlist + \item[\hskip\labelsep{##3##1}]{##3##2\@thmcounterend\ }} + } + +\renewenvironment{abstract}{% + \list{}{\advance\topsep by0.35cm\relax\small + \leftmargin=1cm + \labelwidth=\z@ + \listparindent=\z@ + \itemindent\listparindent + \rightmargin\leftmargin}\item[\hskip\labelsep + \bfseries\abstractname]} + {\endlist} + +\newdimen\headlineindent % dimension for space between +\headlineindent=1.166cm % number and text of headings. + +\def\ps@headings{\let\@mkboth\@gobbletwo + \let\@oddfoot\@empty\let\@evenfoot\@empty + \def\@evenhead{\normalfont\small\rlap{\thepage}\hspace{\headlineindent}% + \leftmark\hfil} + \def\@oddhead{\normalfont\small\hfil\rightmark\hspace{\headlineindent}% + \llap{\thepage}} + \def\chaptermark##1{}% + \def\sectionmark##1{}% + \def\subsectionmark##1{}} + +\def\ps@titlepage{\let\@mkboth\@gobbletwo + \let\@oddfoot\@empty\let\@evenfoot\@empty + \def\@evenhead{\normalfont\small\rlap{\thepage}\hspace{\headlineindent}% + \hfil} + \def\@oddhead{\normalfont\small\hfil\hspace{\headlineindent}% + \llap{\thepage}} + \def\chaptermark##1{}% + \def\sectionmark##1{}% + \def\subsectionmark##1{}} + +\if@runhead\ps@headings\else +\ps@empty\fi + +\setlength\arraycolsep{1.4\p@} +\setlength\tabcolsep{1.4\p@} + +\endinput +%end of file llncs.cls diff --git a/main.blg b/main.blg new file mode 100644 index 0000000..753f880 --- /dev/null +++ b/main.blg @@ -0,0 +1,46 @@ +This is BibTeX, Version 0.99d (TeX Live 2013/Debian) +Capacity: max_strings=35307, hash_size=35307, hash_prime=30011 +The top-level auxiliary file: main.aux +The style file: apalike.bst +Database file #1: markov.bib +You've used 9 entries, + 1935 wiz_defined-function locations, + 534 strings with 5349 characters, +and the built_in function-call counts, 3402 in all, 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[]\T1/ptm/m/it/10 Let $\OML/ptmcm/m/it/10 L +[] \OT1/ptmcm/m/n/10 = + [] + + +Underfull \hbox (badness 5091) in paragraph at lines 582--586 +\OT1/ptmcm/m/n/10 000\OML/ptmcm/m/it/10 ; \OT1/ptmcm/m/n/10 100\OML/ptmcm/m/it/ +10 ; \OT1/ptmcm/m/n/10 101\OML/ptmcm/m/it/10 ; \OT1/ptmcm/m/n/10 001\OML/ptmcm/ +m/it/10 ; \OT1/ptmcm/m/n/10 011\OML/ptmcm/m/it/10 ; \OT1/ptmcm/m/n/10 111\OML/p +tmcm/m/it/10 ; \OT1/ptmcm/m/n/10 110\OML/ptmcm/m/it/10 ; \OT1/ptmcm/m/n/10 010$ + \T1/ptm/m/it/10 be the Gray + [] + + +Underfull \hbox (badness 10000) in paragraph at lines 587--592 +[]\T1/ptm/m/it/10 Let now $\OML/ptmcm/m/it/10 L[] \OT1/ptmcm/m/n/10 = + [] + + +Underfull \hbox (badness 10000) in paragraph at lines 587--592 +\OT1/ptmcm/m/n/10 0100\OML/ptmcm/m/it/10 ; \OT1/ptmcm/m/n/10 1100\OML/ptmcm/m/i +t/10 ; \OT1/ptmcm/m/n/10 1101\OML/ptmcm/m/it/10 ; \OT1/ptmcm/m/n/10 1001\OML/pt +mcm/m/it/10 ; \OT1/ptmcm/m/n/10 1011\OML/ptmcm/m/it/10 ; \OT1/ptmcm/m/n/10 1010 +\OML/ptmcm/m/it/10 ; \OT1/ptmcm/m/n/10 1000$ + [] + + +Underfull \hbox (badness 10000) in paragraph at lines 587--592 +\T1/ptm/m/it/10 be a cyclic Gray code. Since $\OML/ptmcm/m/it/10 S \OT1/ptmcm/m +/n/10 = + [] + + +Underfull \hbox (badness 10000) in paragraph at lines 587--592 +\OT1/ptmcm/m/n/10 2\OML/ptmcm/m/it/10 ; \OT1/ptmcm/m/n/10 3\OML/ptmcm/m/it/10 ; + \OT1/ptmcm/m/n/10 4\OML/ptmcm/m/it/10 ; \OT1/ptmcm/m/n/10 1\OML/ptmcm/m/it/10 +; \OT1/ptmcm/m/n/10 4\OML/ptmcm/m/it/10 ; \OT1/ptmcm/m/n/10 3\OML/ptmcm/m/it/10 + ; \OT1/ptmcm/m/n/10 2\OML/ptmcm/m/it/10 ; \OT1/ptmcm/m/n/10 3\OML/ptmcm/m/it/1 +0 ; \OT1/ptmcm/m/n/10 1\OML/ptmcm/m/it/10 ; \OT1/ptmcm/m/n/10 4\OML/ptmcm/m/it/ +10 ; \OT1/ptmcm/m/n/10 1\OML/ptmcm/m/it/10 ; \OT1/ptmcm/m/n/10 3\OML/ptmcm/m/it +/10 ; \OT1/ptmcm/m/n/10 2\OML/ptmcm/m/it/10 ; \OT1/ptmcm/m/n/10 1\OML/ptmcm/m/i +t/10 ; \OT1/ptmcm/m/n/10 2\OML/ptmcm/m/it/10 ; \OT1/ptmcm/m/n/10 4$ $[][]$ \T1/ +ptm/m/it/10 is equal + [] + + +Underfull \hbox (badness 10000) in paragraph at lines 593--598 +[]\T1/ptm/m/it/10 On the con-trary, for the stan- + [] + + +Underfull \hbox (badness 10000) in paragraph at lines 593--598 +\T1/ptm/m/it/10 dard $\OT1/ptmcm/m/n/10 4$\T1/ptm/m/it/10 -bits Gray code $\OML +/ptmcm/m/it/10 L[] \OT1/ptmcm/m/n/10 = + [] + + +Underfull \hbox (badness 5245) in paragraph at lines 593--598 +\OT1/ptmcm/m/n/10 1101\OML/ptmcm/m/it/10 ; \OT1/ptmcm/m/n/10 1111\OML/ptmcm/m/i +t/10 ; \OT1/ptmcm/m/n/10 1110\OML/ptmcm/m/it/10 ; \OT1/ptmcm/m/n/10 1010\OML/pt +mcm/m/it/10 ; \OT1/ptmcm/m/n/10 1011\OML/ptmcm/m/it/10 ; \OT1/ptmcm/m/n/10 1001 +\OML/ptmcm/m/it/10 ; \OT1/ptmcm/m/n/10 1000$\T1/ptm/m/it/10 , we have + [] + + +Underfull \hbox (badness 4254) in paragraph at lines 607--610 +[]\T1/ptm/m/n/10 Let $\OML/ptmcm/m/it/10 l$ \T1/ptm/m/n/10 be an even pos-i-tiv +e in-te-ger. Find + [] + + +Underfull \hbox (badness 4582) in paragraph at lines 614--619 +\OT1/ptmcm/m/n/10 1\OML/ptmcm/m/it/10 ; n\OT1/ptmcm/m/n/10 )\OML/ptmcm/m/it/10 +; [] ; u[]\OT1/ptmcm/m/n/10 (\OML/ptmcm/m/it/10 u[]; n; n \OMS/pzccm/m/n/10 ^^@ + \OT1/ptmcm/m/n/10 1)$ \T1/ptm/m/n/10 re-spec-tively, where + [] + + +Package amsmath Warning: Foreign command \atopwithdelims; +(amsmath) \frac or \genfrac should be used instead +(amsmath) on input line 637. + +[5] + +LaTeX Warning: Command \textcircled invalid in math mode on input line 726. + + +LaTeX Warning: Command \textcircled invalid in math mode on input line 726. + + +LaTeX Warning: Command \textcircled invalid in math mode on input line 735. + + +LaTeX Warning: Command \textcircled invalid in math mode on input line 735. + + +LaTeX Warning: Command \textcircled invalid in math mode on input line 764. + + +LaTeX Warning: Command \textcircled invalid in math mode on input line 764. + + +LaTeX Warning: Command \textcircled invalid in math 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+\usepackage{subfigure,pstricks,pst-node,pst-coil} +\usepackage{dsfont} +\usepackage{stmaryrd} +\usepackage{cite} +\usepackage{graphicx} +\usepackage{algorithm2e} +\usepackage[font=footnotesize]{subfig} +\usepackage{listings} +\usepackage{booktabs} +\usepackage{epsfig} +\usepackage{url} +\usepackage{calc} +\usepackage{multicol} +\usepackage{pslatex} +\usepackage{apalike} +\usepackage{SCITEPRESS} +\usepackage{caption} + + + +\subfigtopskip=0pt +\subfigcapskip=0pt +\subfigbottomskip=0pt + + + + + + + +\newcommand{\JFC}[1]{\begin{color}{green}\textit{}\end{color}} +\newcommand{\CG}[1]{\begin{color}{blue}\textit{}\end{color}} +\newcommand{\tv}[1] {\lVert #1 \rVert_{\rm TV}} + + +\newtheorem*{xpl}{Running example} +\newtheorem{theorem}{Theorem} + + + + +\newcommand{\vectornorm}[1]{\ensuremath{\left|\left|#1\right|\right|_2}} +\newcommand{\ie}{\textit{i.e.}} +\newcommand{\Nats}[0]{\ensuremath{\mathbb{N}}} +\newcommand{\Reels}[0]{\ensuremath{\mathbb{R}}} +\newcommand{\Bool}[0]{\ensuremath{\mathds{B}}} +\newcommand{\rel}[0]{\ensuremath{{\mathcal{R}}}} +\newcommand{\Gall}[0]{\ensuremath{\mathcal{G}}} + +\begin{document} + +\title{Pseudorandom Number Generators with Balanced Gray Codes} + + +%\author{\authorname{J.-F. Couchot\sup{1}, P.-C. Heam\sup{1}, C. Guyeux\sup{1}, Q. Wang\sup{2}, and J. M. Bahi\sup{1}} +%\affiliation{\sup{1}FEMTO-ST Institute, University of Franche-Comt\'{e}, France} +%\affiliation{\sup{2}College of Automation, Guangdong University of Technology, China } +%\email{\{jean-francois.couchot,pierre-cyrille.heam,christophe.guyeux,jacques.bahi\}@univ-fcomte.fr, wangqianxue@gdut.edu.cn} +%} + +\keywords{Pseudorandom Number Generator, Theory of Chaos, Markov Matrices, Hamiltonian Paths, Mixing Time, Gray Codes, Statistical Tests} + +\abstract{In this article, +it is shown that a large class of truly chaotic Pseudorandom Number Generators +can be constructed. The generators are based on iterating Boolean maps, which are computed +using balanced Gray codes. The number of such Gray codes gives the size of the class. +The construction of such generators is automatic for small number of bits, but remains an open problem when this +number becomes large. A running example is used throughout the paper. Finally, first statistical experiments of these generators are presented, they show how efficient and promising the proposed +approach seems.} + + +\onecolumn \maketitle \normalsize \vfill + + + + + + +\section{\uppercase{Introduction}} + +Many fields of research or applications like numerical simulations, +stochastic optimization, or information security are highly dependent on +the use of fast and unbiased random number generators. Depending on the +targeted application, reproducibility must be either required, leading +to deterministic algorithms that produce numbers as close as possible +to random sequences, or refused, which implies to use an external +physical noise. The formers are called pseudorandom number generators +(PRNGs) while the laters are designed by truly random number generators (TRNGs). +TRNGs are used for instance in cypher keys generation, or in hardware based +simulations or security devices. Such TRNGs are often based on a chaotic +physical signal, may be quantized depending on the application. +This quantization however raises the problem of the degradation of chaotic +properties. + +The use of PRNGs, for its part, is a necessity in a large variety +of numerical simulations, in which +responses of devices under study must be compared using the same ``random'' +stream. This reproducibility is required too for symmetric encryption like +one-time pad, as sender and receiver must share the same pad. However, in +that situation, security of the pseudorandom stream must be mathematically +proven: an attacker must not be able to computationally distinguish a +pseudorandom sequence generated by the considered PRNG with a really random +one. Such cryptographically secure pseudorandom number generators are +however only useful in cryptographic contexts, due to their slowness +resulting from their security. + + +Other kind of properties are desired for PRNGs used in numerical simulations +or in programs that embed a Monte-Carlo algorithm. In these situations, +required properties are speed and random-like profiles of the generated +sequences. The fact that a given PRNG is unbiased and behaves as a white +noise is thus verified using batteries of statistical tests on a large amount +of pseudorandom numbers. Reputed and up-to-date batteries are +currently the NIST suite~\cite{Nist10}, DieHARD~\cite{Marsaglia1996}, +and TestU01~\cite{Simard07testu01:a}, this latter being the +most stringent one. Finally, chaotic properties can be desired when +simulating a chaotic physical phenomenon or in hardware security, in +which cryptographical proofs are not realizable. +In both truly and pseudorandom number generation, there is thus a need +to mathematically guarantee the presence of chaos, and to show that +a post-treatment on a given secure and/or unbiased generator can be realized, +which adds chaos without deflating these desired properties. + + +This work takes place in this domain with the desire of automatically +generating a large class of PRNGs with chaos and statistical properties. +In a sense, it is close to~\cite{BCGR11} where the authors shown that +some Boolean maps may be embedded into an algorithm to provide a PRNG that has both +the theoretical Devaney's chaos property and the practical +property of succeeding NIST statistical battery of tests. +To achieve this, it has been proven in +this article that it is sufficient +for the iteration graph to be strongly connected, +and it is necessary and sufficient for its Markov probability matrix to be doubly stochastic. +However, they do not purpose conditions +to provide such Boolean maps. +Admittedly, sufficient conditions +to retrieve Boolean maps whose graphs are +strongly connected are given, but it remains to further filter those whose +Markov matrix is doubly stochastic. +This approach suffers from delaying the second requirement to a final step +whereas this is a necessary condition. +In this position article, we provide a completely new approach +to generate Boolean functions, whose Markov matrix is doubly stochastic and whose +graph of iterations is strongly connected. +Furthermore the rate of convergence is always taken into consideration to provide +PRNG with good statistical properties. + + +This research work is organized as follows. +It firstly recall some preliminaries that make the document self-contained (Section~\ref{sec:preliminaries}), +The next section (Section~\ref{sec:DSSC}) shows how this problem can be theoretically solved with a classical constraint logic programming. +Section~\ref{sec:hamiltonian} is the strongest contribution of this work. +It presents the main algorithm to generate Boolean maps with all the required properties and +proves that such a construction is correct. +Statistical evaluations are then presented in Section~\ref{sec:exp}. +Conclusive remarks, open problems, and perspectives are +finally provided. + + + + \section{\uppercase{Preliminaries}}\label{sec:preliminaries} + +In what follows, we consider the Boolean algebra on the set +$\Bool=\{0,1\}$ with the classical operators of conjunction '.', +of disjunction '+', of negation '$\overline{~}$', and of +disjunctive union $\oplus$. + +Let $n$ be a positive integer. A {\emph{Boolean map} $f$ is +a function from the Boolean domain + to itself +such that +$x=(x_1,\dots,x_n)$ maps to $f(x)=(f_1(x),\dots,f_n(x))$. +Functions are iterated as follows. +At the $t^{th}$ iteration, only the $s_{t}-$th component is +``iterated'', where $s = \left(s_t\right)_{t \in \mathds{N}}$ is a sequence of indices taken in $\llbracket 1;n \rrbracket$ called ``strategy''. Formally, +let $F_f: \llbracket1;n\rrbracket\times \Bool^{n}$ to $\Bool^n$ be defined by +\[ +F_f(i,x)=(x_1,\dots,x_{i-1},f_i(x),x_{i+1},\dots,x_n). +\] +Then, let $x^0\in\Bool^n$ be an initial configuration +and $s\in +\llbracket1;n\rrbracket^\Nats$ be a strategy, +the dynamics are described by the recurrence +\begin{equation}\label{eq:asyn} +x^{t+1}=F_f(s_t,x^t). +\end{equation} + + +Let be given a Boolean map $f$. Its associated +{\emph{iteration graph}} $\Gamma(f)$ is the +directed graph such that the set of vertices is +$\Bool^n$, and for all $x\in\Bool^n$ and $i\in \llbracket1;n\rrbracket$, +the graph $\Gamma(f)$ contains an arc from $x$ to $F_f(i,x)$. + +\begin{xpl} +Let us consider for instance $n=3$. Let +$f^*: \Bool^3 \rightarrow \Bool^3$ be defined by +$f^*(x_1,x_2,x_3)=(x_2 \oplus x_3, x_1 \oplus \overline{x_3},\overline{x_3})$. +The iteration graph $\Gamma(f^*)$ of this function is given in +Figure~\ref{fig:iteration:f*}. + + +\begin{figure}[ht] + +\begin{center} +\includegraphics[scale=0.5]{iter_f0b.eps} +\end{center} +\caption{Iteration Graph $\Gamma(f^*)$ of the function $f^*$}\label{fig:iteration:f*} + +\end{figure} +\end{xpl} + +It is easy to associate a Markov Matrix $M$ to such a graph $G(f)$ +as follows: +\begin{itemize} +\item $M_{ij} = \frac{1}{n}$ if there is an edge from $i$ to $j$ in $\Gamma(f)$ and $i \neq j$; +\item $M_{ii} = 1 - \sum\limits_{j=1, j\neq i}^n M_{ij}$; +\item $M_{ij} = 0$ otherwise. +\end{itemize} + +\begin{xpl} +The Markov matrix associated to the function $f^*$ is +$$ +\dfrac{1}{3} +\left( +\begin{array}{llllllll} +1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ +1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 \\ +0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 \\ +0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\ +1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ +0 & 0 & 0 & 0 & 1 & 1 & 0 & 1 \\ +0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 \\ +0 & 0 & 0 & 1 & 0 & 0 & 1 & 1 +\end{array} +\right) +$$ + + +\end{xpl} + + +It is usual to check whether rows of such kind of matrices +converge to a specific +distribution. +Let us first recall the \emph{Total Variation} distance $\tv{\pi-\mu}$, +which is defined for two distributions $\pi$ and $\mu$ on the same set +$\Omega$ by: +$$\tv{\pi-\mu}=\max_{A\subset \Omega} |\pi(A)-\mu(A)|.$$ +% It is known that +% $$\tv{\pi-\mu}=\frac{1}{2}\sum_{x\in\Omega}|\pi(x)-\mu(x)|.$$ + +Let then $M(x,\cdot)$ be the +distribution induced by the $x$-th row of $M$. If the Markov chain +induced by +$M$ has a stationary distribution $\pi$, then we define +$$d(t)=\max_{x\in\Omega}\tv{M^t(x,\cdot)-\pi}.$$ +Intuitively $d(t)$ is the largest deviation between +the distribution $\pi$ and $M^t(x,\cdot)$, which +is the result of iterating $t$ times the function. + +Finally, let $\varepsilon$ be a positive number, the \emph{mixing time} +with respect to $\varepsilon$ is given by +$$t_{\rm mix}(\varepsilon)=\min\{t \mid d(t)\leq \varepsilon\}.$$ +It defines the smallest iteration number +that is sufficient to obtain a deviation lesser than $\varepsilon$. +Notice that the upper and lower bounds of mixing times cannot +directly be computed with eigenvalues formulae as expressed +in~\cite[Chap. 12]{LevinPeresWilmer2006}. The authors of this latter work +only consider reversible Markov matrices whereas we do no restrict our +matrices to such a form. + + + +Let us finally present the pseudorandom number generator $\chi_{\textit{14Secrypt}}$ +which is based on random walks in $\Gamma(f)$. +More precisely, let be given a Boolean map $f:\Bool^n \rightarrow \Bool^n$, +a PRNG \textit{Random}, +an integer $b$ that corresponds to an awaited mixing time, and +an initial configuration $x^0$. +Starting from $x^0$, the algorithm repeats $b$ times +a random choice of which edge to follow and traverses this edge. +The final configuration is thus outputted. +This PRNG is formalized in Algorithm~\ref{CI Algorithm}. + + + + +\begin{algorithm}[ht] +%\begin{scriptsize} +\KwIn{a function $f$, an iteration number $b$, an initial configuration $x^0$ ($n$ bits)} +\KwOut{a configuration $x$ ($n$ bits)} +$x\leftarrow x^0$\; +\For{$i=0,\dots,b-1$} +{ +$s\leftarrow{\textit{Random}(n)}$\; +$x\leftarrow{F_f(s,x)}$\; +} +return $x$\; +%\end{scriptsize} +\caption{Pseudo Code of the $\chi_{\textit{14Secrypt}}$ PRNG} +\label{CI Algorithm} +\end{algorithm} + + +This PRNG is a particularized version of Algorithm given in~\cite{BCGR11}. +Compared to this latter, the length of the random +walk of our algorithm is always constant (and is equal to $b$) whereas it +was given by a second PRNG in this latter. +However, all the theoretical results that are given in~\cite{BCGR11} remain +true since the proofs do not rely on this fact. +Let us recall the following theorem. + + + +\begin{theorem}[{\cite[Th. 4, p. 135]{BCGR11}}] + Let $f: \Bool^{n} \rightarrow \Bool^{n}$, $\Gamma(f)$ its + iteration graph, and $M$ its Markov matrix . + If $\Gamma(f)$ is strongly connected, then + the output of the PRNG follows + a law that tends to the uniform distribution + if and only if $M$ is a doubly stochastic matrix. +\end{theorem} + + +With all this material, +we can present an efficient method to +generate Boolean functions +with Doubly Stochastic matrix and Strongly Connected iteration graph, +further (abusively) denoted as DSSC matrix. + + + +\section{\uppercase{Generation of DSSC Matrices}}\label{sec:DSSC} + +This aim of this section is to show +that finding DSSC matrices from a hypercube +is a typical finite domain satisfaction +problem, classically denoted as +Constraint Logic Programming on Finite Domains (CLPFD). +This part is addressed in the first section. Next, we analyse the first +results to provide a generation of DSSC matrices with small mixing times. + +\subsection{Constraint Logic Programming on Finite Domains} + +First of all, +let $n$ be the number of elements. In order to avoid fractions +in this article, we consider here that the +sum of each column and each row is $n$. It can easily be normalized to 1. +The goal is thus to find all the $2^n\times 2^n$ matrices $M$ +such that: + +\begin{enumerate} +\item $M_{ij}$ is 0 if $j$ is not a neighbor of $i$, \textit{i.e.}, + there is no edge from $i$ to $j$ in the $n$-cube. +\item $0 \le M_{ii} \le n$: the number of loops around $i$ is lesser than $n$ +\item Otherwise $0 \le M_{ij} \le 1$: if the edge from $i$ to $j$ is kept, +$M_{ij}$ is 1, and 0 otherwise. +\item For any index of line $i$, $1 \le i\le 2^n$, $n = \sum_{1 \le j\le 2^n} M_{ij}$: + the matrix is right stochastic. +\item For any index of column $j$, + $1 \le j\le 2^n$, $n = \sum_{1 \le i\le 2^n} M_{ij}$: + the matrix is left stochastic. +\item All the values of $\sum_{1\le k\le 2^n}M^k$ are strictly positive, \textit{i.e.}, the induced graph is strongly connected. +\end{enumerate} + + +Since these variables range into finite integer domains with sum and +product operations, this problem can be theoretically handled by +Constraint Logic Programming on Finite Domains (CLPFD), as implemented +in prolog. +The algorithm given in Figure~\ref{fig:prolog} +is indeed the core of the prolog file that is used to instantiate all the solutions +when $n$ is 2. In this code, +\verb+mmult(+$X,Y,R$\verb+)+ and +\verb+summ(+$X,Y,R$\verb+)+ + are true if and only if $R$ is the matrix product + or the matrix sum between + $X$ and $Y$ respectively. It is not hard to adapt such a code to any +value of positive integer $n$. + +\begin{figure}[ht] +\begin{scriptsize} +\lstset{language=prolog} +\begin{lstlisting} +bistoc(X):- + M=[[M0_0, M0_1, 0, M0_3], [M1_0, M1_1, 0, M1_3], + [M2_0, 0, M2_2, M2_3], [0, M3_1, M3_2, M3_3]], + [M0_0, M1_1, M2_2, M3_3] ins 0..2, + [M0_1, M0_3, M1_0, M1_3, M2_0, M2_3, M3_1, M3_2] + ins 0..1, + M0_0+ M0_1+ M0_2 #=2, M1_0+ M1_1+ M1_3 #=2, + M2_0+ M2_2+ M2_3 #=2, M3_1+ M3_2+ M3_3 #=2, + M0_0+ M1_0+ M2_0 #=2, M0_1+ M1_1+ M3_1 #=2, + M0_2+ M2_2+ M3_2 #=2, M1_3+ M2_3+ M3_3 #=2, + mmult(M,M,M2), + mmult(M,M2,M3), + mmult(M,M3,M4), + summ(M,M2,S2), + summ(S2,M3,S3), + summ(S3,M4,S4), + allpositive(S4). +\end{lstlisting} +\end{scriptsize} +\caption{Prolog Problem to Find DSSC Matrix when $n=2$}\label{fig:prolog} +\end{figure} + +Finally, we define the relation $\mathcal{R}$, which is established on the +two functions +$f$ and $g$ if the iteration graphs $\Gamma(f)$ and $\Gamma(g)$ +are isomorphic. +Obviously, this is an equivalence relation. + + + +\subsection{Analysis of the Approach} + +When executed on a personal computer, prolog finds +in less than 1 second the 49 solutions when $n$ is 2, where only 2 are not equivalent, and in less than 1 minute the 27642 solutions where only 111 are +not equivalent when $n$ is 3. But it does not achieve the generation of +all the solutions when $n$ is 4. +This approach suffers from not being efficient enough for large $n$ due to +a \emph{generate and test} approach, despite the efficiency of the native +backtrack of in CLP. + +However, first results for small values of $n$ have been evaluated. +More precisely, non equivalent generated +functions have been compared according to their +ability to efficiently produce uniformly distributed outputs, \textit{i.e.}, +to have the smallest mixing time. + +\begin{xpl} +Table~\ref{table:mixing:3} gives the 5 best Boolean functions +ordered by their mixing times (MT) in the third column for $\varepsilon=10^{-5}$. +\begin{table}[ht] +\begin{small} +$$ +\begin{array}{|l|l|l|} +\hline +\textrm{Name} & \textrm{Image} & \textrm{MT}\\ +\hline +f^* & (x_2 \oplus x_3, x_1 \oplus \overline{x_3},\overline{x_3}) & 16 \\ +\hline +f^a & (x_2 \oplus x_3, \overline{x_1}\overline{x_3} + x_1\overline{x_2}, +\overline{x_1}\overline{x_3} + x_1x_2) & 17 \\ +\hline +f^b & (\overline{x_1}(x_2+x_3) + x_2x_3,\overline{x_1}(\overline{x_2}+\overline{x_3}) + \overline{x_2}\overline{x_3}, & \\ +& \qquad \overline{x_3}(\overline{x_1}+x_2) + \overline{x_1}x_2) & 26 \\ +\hline +f^c & (\overline{x_1}(x_2+x_3) + x_2x_3,\overline{x_1}(\overline{x_2}+\overline{x_3}) + \overline{x_2}\overline{x_3}, & \\ +& \overline{x_3}(\overline{x_1}+x_2) + \overline{x_1}x_2) & 29 \\ +\hline +f^d & (x_1\oplus x_2,x_3(\overline{x_1}+\overline{x_2}),\overline{x_3}) & 30 \\ +\hline +% [3, 4, 7, 0, 1, 6, 5, 2], #16 +% [3, 4, 7, 0, 2, 6, 5, 1], #17 +% [3, 6, 7, 5, 2, 0, 1, 4], #26 +% [3, 4, 7, 5, 2, 6, 1, 0], #29 +% [3, 2, 5, 6, 7, 0, 1, 4]] #30 +\end{array} +$$ +\end{small} +\caption{The 5 Boolean functions with smallest MT when $n=3$.}\label{table:mixing:3} +\end{table} +\end{xpl} + +A syntactical analysis of the functions for $n$=3 +does not help to understand +how to build a Boolean map with a small mixing time. +However the iteration graph of $f^*$ +(given in Figure~\ref{fig:iteration:f*}) +is the $3$-cube in which the cycle +$000,100,101,001,011,111,110,010,000$ +has been removed. +This cycle that visits each vertex exactly once is usually denotes as +\emph{Hamiltonian cycle}. +We are now focusing on the generation of DSSC matrices by +removing Hamiltonian cycles of the $n$-cube. This is the aims of the next +section. + + +\section{\uppercase{Removing Hamiltonian Cycles}}\label{sec:hamiltonian} +This section addresses the problem of removing an Hamiltonian path in the $n$-cube. +The first theoretical section shows that this approach produces DSSC matrix, as wished. +The motivation to focus on balanced Gray code is then given in Sec.~\ref{sub:gray}. +We end this section by recalling an algorithm that aims at computing such codes (Section~\ref{sub:algo:gray}). + +\subsection{Theoretical Aspects of Removing Hamiltonian Cycles} + +We first have the following result on stochastic matrix and $n$-cube without +Hamiltonian cycle. + +\begin{theorem} +The Markov Matrix $M$ resulting from the $n$-cube in +which an Hamiltonian +cycle is removed, is doubly stochastic. +\end{theorem} +\begin{proof} +An Hamiltonian cycle visits each vertex exactly once. +For each vertex $v$ in the $n$-cube, +one ongoing edge $(o,v)$ and one outgoing edge $(v,e)$ +are thus removed. + +Let us consider the Markov matrix $M$ of the $n$-cube. +It is obviously doubly stochastic. +Since we exactly remove one outgoing edge, the value of $M_{ve}$ decreases +from $\frac{1}{n}$ to 0 and +$M_{vv}$ is $\frac{1}{n}$. The $M$ matrix is stochastic again. +Similarly for ongoing edge, since one ongoing edge is dropped for each +vertex, the value of $M_{ov}$ decreases +from $\frac{1}{n}$ to $0$. Moreover, since $M_{vv}$ is $\frac{1}{n}$, +the sum of values in column $v$ is $1$, and $M$ is doubly stochastic. +\end{proof} + +The following result states that the $n$-cube without one +Hamiltonian cycle +has the awaited property with regard to the connectivity. + +\begin{theorem} +The iteration graph issued from the $n$-cube where an Hamiltonian +cycle is removed is strongly connected. +\end{theorem} +\begin{proof} +We consider the reverse cycle $r$ of the Hamiltonian cycle $c$. +There is no edge that belongs to both $r$ and $c$: otherwise $c$ +would contain one vertex twice. Thus, no edges of $r$ has been removed. +The cycle $r$ is obviously an Hamiltonian cycle and contains all the nodes. +Any node of the $n$-cube where $c$ has been removed can thus reach any node. +The iteration graph is thus strongly connected. +\end{proof} + +Removing an Hamiltonian cycle in the $n$-cube solves thus the DSSC constraint. +We are then left to focus on the generation of Hamiltonian cycles in the +$n$-cube. Such a problem is equivalent to find Gray codes, \textit{i.e.}, +to find a sequence of $2^n$ codewords ($n$-bits strings) +where two successive elements differ in only one bit position. +The next section is dedicated to these codes. + +\subsection{Linking to (Totally) Balanced Gray Codes}\label{sub:gray} +Many research works~\cite{journals/combinatorics/BhatS96,VanSup04,journals/combinatorics/FlahiveB07} +have addressed the subject of finding Gray codes. +Since our approach is based on removing a cycle, we are concerned +with cyclic Gray codes, \textit{i.e.}, sequences where the last codeword +differs in only one bit position from the first one. + +Let $n$ be a given integer. As far as we know, +the exact number of Gray codes in $\Bool^n$ is not known but +a lower bound, $$\left(\frac{n*\log2}{e \log \log n}*(1 - o(1))\right)^{2^n}$$ +has been given in~\cite{Feder:2009:NTB:1496397.1496515}. +For example, when $n$ is $6$, such a number is larger than $10^{13}$. + +To avoid this combinatorial explosion, we want to +restrict the generation to any Gray code +such that the induced graph of iteration $\Gamma(f)$ is +``uniform''. In other words, if we count in $\Gamma(f)$ +the number of edges that modify the bit $i$, for $1 \le i \le n$, +all these values have to be close to each other. +Such an approach is equivalent to restrict the search of cyclic Gray codes +which are uniform too. + +This notion can be formalized as follows. Let $L = w_1, w_2, \dots, w_{2^n}$ be the sequence +of a $n$-bits cyclic Gray code. Let $S = s_1, s_2, \dots, s_{2^n}$ be the +transition sequence where $s_i$, $1 \le i \le 2^n$ indicates which bit position changes between +codewords at index $i$ and $i+1$ modulo $2^n$. +Let $\textit{TC}_n : \{1,\dots, n\} \rightarrow \{0, \ldots, 2^n\}$ the \emph{transition count} function +that counts the number of times $i$ occurs in $S$, \textit{i.e.}, the number of times +the bit $i$ has been switched in $L$. +The Gray code is \emph{totally balanced} if $\textit{TC}_n$ is constant (and equal to $\frac{2^n}{n}$). +It is \emph{balanced} if for any two bit indices $i$ and $j$, +$|\textit{TC}_n(i) - \textit{TC}_n(j)| \le 2$. + +\begin{xpl} +Let $L^*=000,100,101,001,011,111,110,010$ be the Gray code that corresponds to +the Hamiltonian cycle that has been removed in $f^*$. +Its transition sequence is $S=3,1,3,2,3,1,3,2$ and its transition count function is +$\textit{TC}_3(1)= \textit{TC}_3(2)=2$ and $\textit{TC}_3(3)=4$. Such a Gray code is balanced. + +Let now +$L^4=0000, 0010, 0110, 1110, 1111, 0111, 0011, 0001, 0101,$ +$0100, 1100, 1101, 1001, 1011, 1010, 1000$ +be a cyclic Gray code. Since $S=2,3,4,1,4,3,2,3,1,4,1,3,2,1,2,4$ $\textit{TC}_4$ is equal to 4 everywhere, this code +is thus totally balanced. + +On the contrary, for the standard $4$-bits Gray code +$L^{\textit{st}}=0000,0001,0011,0010,0110,0111,0101,0100,1100,$ +$1101,1111,1110,1010,1011,1001,1000$, +we have $\textit{TC}_4(1)=8$ $\textit{TC}_4(2)=4$ $\textit{TC}_4(3)=\textit{TC}_4(4)=2$ and +the code is neither balanced nor totally balanced. +\end{xpl} + +\subsection{Induction-Based Generation of Balanced Gray Codes}\label{sub:algo:gray} +The algorithm we adapt is based on the ``Construction B''~\cite{VanSup04} we recall now. +This method inductively constructs $n$-bits Gray code given a $n-2$-bit Gray code. + +It starts with the transition sequence $S_{n-2}$ of such code. + +\begin{enumerate} +\item \label{item:nondet}Let $l$ be an even positive integer. Find +$u_1, u_2, \dots , u_{l-2}, v$ (maybe empty) subsequences of $S_{n-2}$ +such that $S_{n-2}$ is the concatenation of +$$ +s_{i_1}, u_0, s_{i_2}, u_1, s_{i_3}, u_2, . . . , s_{i_l-1}, u_{l-2}, s_{i_l}, v +$$ +where $i_1 = 1$, $i_2 = 2$, and $u_0 = \emptyset$ (the empty sequence). +\item Replace in $S_{n-2}$ the sequences $u_0, u_1, u_2, \ldots, u_{l-2}$ + by + $n - 1, u'(u_1,n - 1, n) , u'(u_2,n, n - 1), u'(u_3,n - 1,n), \dots, u'(u_{l-2},n, n - 1)$ + respectively, where $u'(u,x,y)$ is the sequence $u,x,u^R,y,u$ such that + $u^R$ is $u$ in reversed order. The obtained sequence is further denoted as $U$. +\item Construct the sequences $V=v^R,n,v$, $W=n-1,S_{n-2},n$, and let $W'$ be $W$ where the first +two elements have been exchanged. +\item The transition sequence $S_{n}$ is thus the concatenation $U^R, V, W'$. +\end{enumerate} + +It has been proven in~\cite{VanSup04} that +$S_{n}$ is transition sequence of a cyclic $n$-bits Gray code +if $S_{n-2}$ is. +However, the step~\ref{item:nondet} is not a constructive +step that precises how to select the subsequences which ensures that +yielded Gray code is balanced. + +Let us now evaluate the number of subsequences $u$ +than can be produced. Since $s_{i_1}$ and $s_{i_2}$ are well +defined, we have to chose the $l-2$ elements of $s_3,s_4,\dots,s_{2^{n-2}}$ +that become $s_{i_3},\dots, s_{i_l}$. Let $l = 2l'$. +There are thus +$$ +\#_n = \sum_{l'=1}^{2^{n-3}} {2^{n-2}-2 \choose 2l'-2} +$$ +distinct subsequences $u$. +Numerical values of $\#_n$ are given in table~\ref{table:combinations}. +Even for small values of $n$, it is not reasonable to hope to evaluate the whole +set of subsequences. +\begin{table}[ht] +\begin{center} +\begin{tabular}{|l|l|l|l|l|l|l|l|l|} +\hline +$n$ & 5 & 6 & 7 & 8 & 9 \\ +\hline +$\#_n$ & +31 & 8191 & 5.3e8 & 2.3e18 & 4.2e37\\ +\hline +$\#'_n$ & +15 & 3003 & 1.4e8 & 4.5e17 & 1.6e36 \\ +\hline +\end{tabular} +\end{center} +\caption{Number of distinct $u$ subsequences.}\label{table:combinations} +\end{table} + +However, it is shown in the article that $\textit{TC}_n(n-1)$ and $\textit{TC}_n(n)$ are +equal to $l$. Since this step aims at generating (totally) balanced Gray codes, +we have set $l$ to be the largest even integer less or equal than $\frac{2^n}{n}$. +This improvement allows to reduce the number of subsequences to study. +Examples of such cardinalities are given in table~\ref{table:combinations} and are refered as +$\#'_n$. + +Finally, the table~\ref{table:nbFunc} gives the number of non-equivalent functions issued from +(totally) balanced Gray codes that can be generated +with the approach presented in this article with respect to the number of bits. In other words, it corresponds to the size of the class of generators that can be produced. + +\begin{table}[ht] +\begin{center} +\begin{tabular}{|l|c|c|c|c|} +\hline +$n$ & 3 & 4 & 5 & 6 \\ +\hline +nb. of functions & 1 & 1 & 2 & 1332 \\ +\hline +\end{tabular} +\end{center} +\caption{Number of Generators w.r.t. the number of bits.} +\label{table:nbFunc} +\end{table} + + +\section{\uppercase{Experiments}}\label{sec:exp} +We present in Algorithm~\ref{CI} the method +that allows to take any chaotic function as the core of a pseudo +random number generator. Among the parameters, it takes the +number b of minimal iterations that have to be executed to +get a uniform like distribution. 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+\usepackage[T1]{fontenc} +\usepackage[english]{babel} +\usepackage{amsmath,amssymb,latexsym,eufrak,euscript} +\usepackage{subfigure,pstricks,pst-node,pst-coil} + + +\usepackage{url,tikz} +\usepackage{pgflibrarysnakes} + +\usepackage{multicol} + +\usetikzlibrary{arrows} +\usetikzlibrary{automata} +\usetikzlibrary{snakes} +\usetikzlibrary{shapes} + +%% \setlength{\oddsidemargin}{15mm} +%% \setlength{\evensidemargin}{15mm} \setlength{\textwidth}{140mm} +%% \setlength{\textheight}{219mm} \setlength{\topmargin}{5mm} +\newtheorem{theorem}{Theorem} +%\newtheorem{definition}[theorem]{Definition} +% %\newtheorem{defis}[thm]{D\'efinitions} + \newtheorem{example}[theorem]{Example} +% %\newtheorem{Exes}[thm]{Exemples} +\newtheorem{lemma}[theorem]{Lemma} +\newtheorem{proposition}[theorem]{Proposition} +\newtheorem{construction}[theorem]{Construction} +\newtheorem{corollary}[theorem]{Corollary} +% \newtheorem{algor}[thm]{Algorithm} +%\newtheorem{propdef}[thm]{Proposition-D\'efinition} +\newcommand{\mlabel}[1]{\label{#1}\marginpar{\fbox{#1}}} +\newcommand{\flsup}[1]{\stackrel{#1}{\longrightarrow}} + +\newcommand{\stirlingtwo}[2]{\genfrac{\lbrace}{\rbrace}{0pt}{}{#1}{#2}} +\newcommand{\stirlingone}[2]{\genfrac{\lbrack}{\rbrack}{0pt}{}{#1}{#2}} + +\newenvironment{algo} +{ \vspace{1em} +\begin{algor}\mbox +\newline \vspace{-0.1em} +\begin{quote}\begin{rm}} +{\end{rm}\end{quote}\end{algor}\vspace{-1.5em}\vspace{2em}} +%\null \hfill $\diamondsuit$ \par\medskip \vspace{1em}} + +\newenvironment{exe} +{\begin{example}\rm } +{\end{example} +%\vspace*{-1.5em} +%\null \hfill $\triangledown$ \par\medskip} +%\null \hfill $\triangledown$ \par\medskip \vspace{1em}} +} + + +\newenvironment{proof} +{ \noindent {\sc Proof.\/} } +{\null \hfill $\Box$ \par\medskip \vspace{1em}} + + +\newcommand {\pb}[3] { +\medskip +\noindent +\fbox{ +\parbox[c]{11.5cm}{ +{\bf #1} + +\noindent +{\bf Input:} #2 + +\noindent +{\bf Output:} #3 + +\medskip +} +} + +\medskip +} + + +\newcommand {\tv}[1] {\lVert #1 \rVert_{\rm TV}} +\def \top {1.8} +\def \topt {2.3} +\def \sp {\hspace*{0.8cm}} +\def \A {\mathcal{A}} +\def \P {\mathcal{P}} +\def \B {\mathcal{B}} +\def \C {\mathcal{C}} +\def \D {\mathcal{D}} +\def \R {\mathcal{R}} +\def \T {\mathfrak{T}} +\def \M {\mathcal{M}} +\def \ov {\overline} + +\begin{document} +\label{firstpage} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Mathematical Backgroung} + +Let $G$ be a finite group. For any subset $S$ of $G$ we denote by +$$ the subgroup of $G$ generated by $S$. +If $=G$, $S$ is a generator of $G$. + + + +Let $\pi$, $\mu$ be two distribution on a same set $\Omega$. The total +variation distance between $\pi$ and $\mu$ is denoted $\tv{\pi-\mu}$ and is +defined by +$$\tv{\pi-\mu}=\max_{A\subset \Omega} |\pi(A)-\mu(A)|.$$ It is known that +$$\tv{\pi-\mu}=\frac{1}{2}\sum_{x\in\Omega}|\pi(x)-\mu(x)|.$$ Moreover, if +$\nu$ is a distribution on $\Omega$, one has +$$\tv{\pi-\mu}\leq \tv{\pi-\nu}+\tv{\nu-\mu}$$ + +Let $P$ be the matrix of a markov chain on $\Omega$. $P(x,\cdot)$ is the +distribution induced by the $x$-th row of $P$. If the markov chain induced by +$P$ has a stationary distribution $\pi$, then we define +$$d(t)=\max_{x\in\Omega}\tv{P^t(x,\cdot)-\pi},$$ +and + +$$t_{\rm mix}(\varepsilon)=\min\{t \mid d(t)\leq \varepsilon\}.$$ +One can prove that + +$$t_{\rm mix}(\varepsilon)\leq \lceil\log_2(\varepsilon^{-1})\rceil t_{\rm mix}(\frac{1}{4})$$ + +It is known that $d(t+1)\leq d(t)$. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{PRNG and random walk on Cayley graphs} + + +Let $S$ be a generator of $\mathbb{B}^N$ such that if $s\in S$, then +$-s\in S$. Let $\nu$ be a distribution on $S$ such that +$\nu(s)=\nu(-s)$. The matrix $P^\nu$, or just $P^\nu$, or just $P$, +is the matrix defined by: $P^\nu(x,y)=\nu(y-x)$ if $x-y\in S$ and $0$ +otherwise. $P_S^\nu$ is the $\nu$-random walk on the $S$-Cayley graph +of $G$. + +A general results on random walks claims that the uniform distribution +is stationnary for $P$. Moreover, if $\nu(s)>0$ for each $s$, then +this is the limit distribution. + +Let $\mathcal{P}$ be finite subset of $\mathbb{N}$ and $\mu$ a distribution +on $\mathcal{P}$. Set +$$ P_{\mathcal{P},\mu}=\sum_{k\in\mathcal{P}}\mu(k)P^k.$$ + + +With the above notation, $P_{\mathcal{P},\mu}$ is the matrix of the markov +chain corresponding to the PRNG defined by Christophe, where $S$ corresponds +to the boolean functions and $\mu$ si the probability of choosing elements +of $\mathcal{P}$. + + +\begin{exe} +For instance let $e_i$ be the vector of $\mathbb{B}^N$ whose $i$-th +componenent is $1$ and all other compoennts are null. Let $e_0=0$ and +$S=\{e_i\mid 0\leq i\leq N\}$. Choosing $\nu(e_i)=\dfrac{1}{N+1}$, we +obtain the random walk defined by the {\em bit negation} of the paper +by Christophe and JEF. +The associated matrix will be denoted $P_1$. + Choosing $\mathcal{P}=\{10,11\}$ and +$\mu(10)=\mu(11)=\dfrac{1}{2}$ provides the PRNG with steps of lengths +10 or 11 with the same probability. +\end{exe} + + +\begin{exe} +With the same notation, choosing the same $S$, but +$\nu(e_i)=\dfrac{1}{2n}$ if $i \geq 1$ and $\nu(e_0)=1/2$ leads to the +the classical lazy random walk on $\mathbb{B}^N$ (also known as the +lazy random walk on the hypercube or as the Ehrenfest Urn Model). +The associated matrix will be denoted $P_2$. +\end{exe} + +\begin{exe} +Choosing $S=G$ and the uniform distribution for $\nu$ corresponds to +the xor approach of the paper with Raphael. +\end{exe} + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Results} + +The main result is that if the minimal element of $\mathcal{P}$ is +greater or equal to the mixing time of $P$, then the PRNG provides a distribution +whose distance to the uniform distribution is at most $\varepsilon$. + +Let $t_P(\varepsilon)$ be the $\varepsilon$ mixing time for $P$. +Without loss of generality we assume that if $k\in \mathcal{P}$, then +$\mu(k)>0$. + +\begin{proposition} +Let $k_0=\min \{ k\mid k\in \mathcal{P}\}$. +If $k_0 \geq +t_P(\varepsilon)$, and if $\nu(s)>0$ for all $s\in S$, then one has +$\tv{P_{\mathcal{P},\mu}(x,\cdot)-\pi}\leq \varepsilon$, where $\pi$ +is the uniform distribution. +\end{proposition} + +\begin{proof} +The fact that $\nu(s)>0$ for all $s\in S$ ensures that the uniform +distribution is the limits of the markov chains induced by $P$ +(classical results on random walks). + +Now, +\begin{align*} +\tv{P_{\mathcal{P},\mu}(x,\cdot)-\pi}&=\tv{\sum_{k\in\mathcal{P}}\mu(k)P^k(x,\cdot)-\pi}\\ +&=\frac{1}{2}\sum_{y\in\mathbb{B}^N}|\sum_{k\in\mathcal{P}}\mu(k)P^k(x,y)-\dfrac{1}{2^N}|\\ +&=\frac{1}{2}\sum_{y\in\mathbb{B}^N}|\sum_{k\in\mathcal{P}}\mu(k)P^k(x,y)-\dfrac{1}{2^N}\sum_{k\in\mathcal{P}}\mu(k)|\\ +&=\frac{1}{2}\sum_{y\in\mathbb{B}^N}|\sum_{k\in\mathcal{P}}\mu(k)(P^k(x,y)-\dfrac{1}{2^N})|\\ +&\leq \frac{1}{2}\sum_{y\in\mathbb{B}^N}\sum_{k\in\mathcal{P}}\mu(k)|P^k(x,y)-\dfrac{1}{2^N}|\\ +&\leq \sum_{k\in\mathcal{P}}\mu(k)\left(\frac{1}{2}\sum_{y\in\mathbb{B}^N}|P^k(x,y)-\dfrac{1}{2^N}|\right)\\ +&\leq \sum_{k\in\mathcal{P}}\mu(k)\tv{P^k(x,\cdot)-\pi}\\ +&\leq \sum_{k\in\mathcal{P}}\mu(k)\varepsilon\\ +&\leq \varepsilon\\ +\end{align*} +\end{proof} + + +Therfore it suffices to study the mixing time of $P$. + + + +%%%%%%%%%%%%%%%%%%%% +\section{Mixing time of $P_1$} + +See the Ehrenfest Urn Model. One can prove that for $P_1$, + +$$t_{\rm mix}(\varepsilon)\leq N \log N+ \log (\frac{1}{\varepsilon})N.$$ + +Better results exist see \cite[page 83, page 267]{mixing} + +%%%%%%%%%%%%%%%%%%%% +\section{Mixing time of $P_2$} + +In practice one can compute egenvalues and use \cite[page 155]{mixing}. + +There are theoretical results \cite[page 321-322]{rwfg} and~\cite{WilsonHyper}. + + +%%%%%%%%%%%%%%%%%%%% +\section{To do} + +Experiments for computing mixing time for $P_2$. + +Experiments for other $P$ (handly built) + +Which $\varepsilon$ makes possible to pass statistical tests for our PRNGs. Other tests can be performed. + +%%%%%%%%%%%%%%%%%%%%%% +\section{Future} + +Look at \cite{rwfg} for theoretical results. Explore random random walk on the hypercube. + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\bibliographystyle{alpha} +\bibliography{markovbib} +\end{document}