From: Pierre-Cyrille Héam Date: Wed, 22 Jun 2016 12:45:04 +0000 (+0200) Subject: pch X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/16dcc.git/commitdiff_plain/66ea391a3e386a6ed3b47d5011977ca136f65ad2?hp=2cf19b6a4aa1800981fa0b35e6f555119b94910e pch --- diff --git a/main.aux b/main.aux index 0bd4d61..a426c9e 100644 --- a/main.aux +++ b/main.aux @@ -38,13 +38,13 @@ \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.2}{A Metric Space for PRNG Iterations}}{5}} \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.3}{A metric on $\mathcal {X}_{\mathsf {N},\mathcal {P}}$}}{6}} \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.4}{$\Gamma _{\mathcal {P}}(f)$ as an extension of $\Gamma (f)$}}{8}} -\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.5}{Proofs of chaos}}{8}} \newlabel{graphe1}{{2a}{9}} \newlabel{sub@graphe1}{{a}{9}} \newlabel{graphe2}{{2b}{9}} \newlabel{sub@graphe2}{{b}{9}} \@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Iterating $f_0:(x_1,x_2) \DOTSB \mapstochar \rightarrow (\overline {x_1}, \overline {x_2})$\relax }}{9}} \newlabel{fig:itg}{{2}{9}} +\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.5}{Proofs of chaos}}{9}} \newlabel{prop:trans}{{3.8}{9}} \citation{bcgr11:ip} \citation{DBLP:conf/secrypt/CouchotHGWB14} @@ -69,33 +69,33 @@ \citation{ZanSup04} \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{5.1}{Analysis of the Robinson-Cohn extension algorithm}}{12}} \newlabel{item:nondet}{{1}{12}} -\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{5.2}{Balanced Codes}}{12}} +\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{5.2}{Balanced Codes}}{13}} \newlabel{prop:balanced}{{5.1}{13}} -\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{5.3}{Toward a local uniform distribution of switches}}{13}} -\@writefile{toc}{\contentsline {section}{\tocsection {}{6}{Stopping Time}}{13}} -\newlabel{sec:hypercube}{{6}{13}} \citation{LevinPeresWilmer2006} +\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{5.3}{Toward a local uniform distribution of switches}}{14}} +\@writefile{toc}{\contentsline {section}{\tocsection {}{6}{Stopping Time}}{14}} +\newlabel{sec:hypercube}{{6}{14}} +\newlabel{thm-sst}{{6.1}{15}} \newlabel{eq:Markov:rairo}{{3}{15}} -\newlabel{lm:h}{{6.2}{15}} -\citation{proba} +\newlabel{lm:h}{{6.2}{16}} \newlabel{prop:stop}{{6.4}{16}} \newlabel{prop:lambda}{{6.5}{16}} +\citation{proba} \newlabel{lm:stopprime}{{6.6}{17}} \@writefile{toc}{\contentsline {section}{\tocsection {}{7}{Experiments}}{18}} \newlabel{sec:prng}{{7}{18}} \@writefile{loa}{\contentsline {algocf}{\numberline {2}{\ignorespaces Pseudo Code of the $\chi _{\textit {15Rairo}}$ PRNG\relax }}{18}} \newlabel{CI Algorithm:2}{{2}{18}} -\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces Functions with DSCC Matrix and smallest MT\relax }}{19}} -\newlabel{table:nc}{{1}{19}} +\@writefile{toc}{\contentsline {section}{\tocsection {}{8}{Conclusion}}{19}} \bibstyle{alpha} \bibdata{biblio} \bibcite{Banks92}{BBCS92} -\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces NIST SP 800-22 test results ($\mathbb {P}_T$)\relax }}{20}} -\newlabel{The passing rate}{{2}{20}} -\@writefile{toc}{\contentsline {section}{\tocsection {}{8}{Conclusion}}{20}} \bibcite{bcgr11:ip}{BCGR11} \bibcite{Nist10}{BR10} \bibcite{DBLP:journals/combinatorics/BhatS96}{BS96} +\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces Functions with DSCC Matrix and smallest MT\relax }}{20}} +\newlabel{table:nc}{{1}{20}} +\@writefile{toc}{\contentsline {section}{\tocsection {}{}{References}}{20}} \bibcite{Bykov2016}{Byk16} \bibcite{chgw14oip}{CHG{$^{+}$}14a} \bibcite{DBLP:conf/secrypt/CouchotHGWB14}{CHG{$^{+}$}14b} @@ -106,12 +106,13 @@ \bibcite{LEcuyerS07}{LS07} \bibcite{Marsaglia1996}{Mar96} \bibcite{proba}{MU05} +\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces NIST SP 800-22 test results ($\mathbb {P}_T$)\relax }}{21}} +\newlabel{The passing rate}{{2}{21}} \bibcite{Robinson:1981:CS}{RC81} \bibcite{915385}{SK01} \bibcite{915396}{SPK01} \bibcite{ZanSup04}{SZ04} \bibcite{wbg10ip}{WBGF10} -\@writefile{toc}{\contentsline {section}{\tocsection {}{}{References}}{21}} \newlabel{tocindent-1}{0pt} \newlabel{tocindent0}{12.77466pt} \newlabel{tocindent1}{17.77344pt} diff --git a/main.blg b/main.blg index 01af0c2..d3e8eb8 100644 --- a/main.blg +++ b/main.blg @@ -1,4 +1,4 @@ -This is BibTeX, Version 0.99d (TeX Live 2015/dev/Debian) +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: alpha.bst diff --git a/main.log b/main.log index 24b84b6..633dfbf 100644 --- a/main.log +++ b/main.log @@ -1,11 +1,11 @@ -This is pdfTeX, Version 3.14159265-2.6-1.40.15 (TeX Live 2015/dev/Debian) (preloaded format=pdflatex 2015.4.13) 7 APR 2016 20:24 +This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013/Debian) (format=pdflatex 2014.6.13) 22 JUN 2016 14:44 entering extended mode restricted \write18 enabled. %&-line parsing enabled. **main.tex (./main.tex -LaTeX2e <2014/05/01> -Babel <3.9l> and hyphenation patterns for 79 languages loaded. +LaTeX2e <2011/06/27> +Babel <3.9h> and hyphenation patterns for 78 languages loaded. (./ita.cls Document Class: ita 1999/03/01 v1.1 EDP-Sciences (/usr/share/texlive/texmf-dist/tex/latex/amscls/amsart.cls @@ -127,10 +127,10 @@ Package: cite 2010/09/10 v 5.3 \c@thrm=\count104 ) (/usr/share/texlive/texmf-dist/tex/latex/graphics/graphicx.sty -Package: graphicx 2014/04/25 v1.0g Enhanced LaTeX Graphics (DPC,SPQR) +Package: graphicx 1999/02/16 v1.0f Enhanced LaTeX Graphics (DPC,SPQR) (/usr/share/texlive/texmf-dist/tex/latex/graphics/keyval.sty -Package: keyval 2014/05/08 v1.15 key=value parser (DPC) +Package: keyval 1999/03/16 v1.13 key=value parser (DPC) \KV@toks@=\toks25 ) (/usr/share/texlive/texmf-dist/tex/latex/graphics/graphics.sty @@ -190,22 +190,22 @@ LaTeX Font Info: Overwriting symbol font `stmry' in version `bold' (Font) U/stmry/m/n --> U/stmry/b/n on input line 89. ) (/usr/share/texlive/texmf-dist/tex/latex/base/ifthen.sty -Package: ifthen 2014/09/29 v1.1c Standard LaTeX ifthen package (DPC) +Package: ifthen 2001/05/26 v1.1c Standard LaTeX ifthen package (DPC) ) (/usr/share/texlive/texmf-dist/tex/latex/graphics/color.sty -Package: color 2014/04/23 v1.1a Standard LaTeX Color (DPC) +Package: color 2005/11/14 v1.0j Standard LaTeX Color (DPC) (/usr/share/texlive/texmf-dist/tex/latex/latexconfig/color.cfg File: color.cfg 2007/01/18 v1.5 color configuration of teTeX/TeXLive ) -Package color Info: Driver file: pdftex.def on input line 137. +Package color Info: Driver file: pdftex.def on input line 130. ) (/usr/share/texlive/texmf-dist/tex/latex/algorithm2e/algorithm2e.sty Package: algorithm2e 2013/01/06 v5.00 algorithms environments \c@AlgoLine=\count109 (/usr/share/texlive/texmf-dist/tex/latex/tools/xspace.sty -Package: xspace 2014/10/28 v1.13 Space after command names (DPC,MH) +Package: xspace 2009/10/20 v1.13 Space after command names (DPC,MH) ) (/usr/share/texlive/texmf-dist/tex/latex/relsize/relsize.sty Package: relsize 2013/03/29 ver 4.1 @@ -305,19 +305,19 @@ File: epstopdf-sys.cfg 2010/07/13 v1.3 Configuration of (r)epstopdf for TeX Liv e ))) (/usr/share/texlive/texmf-dist/tex/latex/base/inputenc.sty -Package: inputenc 2014/04/30 v1.2b Input encoding file +Package: inputenc 2008/03/30 v1.1d Input encoding file \inpenc@prehook=\toks26 \inpenc@posthook=\toks27 (/usr/share/texlive/texmf-dist/tex/latex/base/utf8.def -File: utf8.def 2014/09/29 v1.1m UTF-8 support for inputenc +File: utf8.def 2008/04/05 v1.1m UTF-8 support for inputenc Now handling font encoding OML ... ... no UTF-8 mapping file for font encoding OML Now handling font encoding T1 ... ... processing UTF-8 mapping file for font encoding T1 (/usr/share/texlive/texmf-dist/tex/latex/base/t1enc.dfu -File: t1enc.dfu 2014/09/29 v1.1m UTF-8 support for inputenc +File: t1enc.dfu 2008/04/05 v1.1m UTF-8 support for inputenc defining Unicode char U+00A1 (decimal 161) defining Unicode char U+00A3 (decimal 163) defining Unicode char U+00AB (decimal 171) @@ -467,7 +467,7 @@ Now handling font encoding OT1 ... ... processing UTF-8 mapping file for font encoding OT1 (/usr/share/texlive/texmf-dist/tex/latex/base/ot1enc.dfu -File: ot1enc.dfu 2014/09/29 v1.1m UTF-8 support for inputenc +File: ot1enc.dfu 2008/04/05 v1.1m UTF-8 support for inputenc defining Unicode char U+00A1 (decimal 161) defining Unicode char U+00A3 (decimal 163) defining Unicode char U+00B8 (decimal 184) @@ -498,7 +498,7 @@ Now handling font encoding OMS ... ... processing UTF-8 mapping file for font encoding OMS (/usr/share/texlive/texmf-dist/tex/latex/base/omsenc.dfu -File: omsenc.dfu 2014/09/29 v1.1m UTF-8 support for inputenc +File: omsenc.dfu 2008/04/05 v1.1m UTF-8 support for inputenc defining Unicode char U+00A7 (decimal 167) defining Unicode char U+00B6 (decimal 182) defining Unicode char U+00B7 (decimal 183) @@ -529,13 +529,13 @@ File: t1enc.def 2005/09/27 v1.99g Standard LaTeX file LaTeX Font Info: Redeclaring font encoding T1 on input line 43. )) (/usr/share/texlive/texmf-dist/tex/generic/babel/babel.sty -Package: babel 2014/09/25 3.9l The Babel package +Package: babel 2013/12/03 3.9h The Babel package (/usr/share/texlive/texmf-dist/tex/generic/babel-english/english.ldf Language: english 2012/08/20 v3.3p English support from the babel system (/usr/share/texlive/texmf-dist/tex/generic/babel/babel.def -File: babel.def 2014/09/25 3.9l Babel common definitions +File: babel.def 2013/12/03 3.9h Babel common definitions \babel@savecnt=\count113 \U@D=\dimen129 ) @@ -571,15 +571,13 @@ Package: pstricks 2013/12/12 v0.60 LaTeX wrapper for `PSTricks' (RN,HV) File: pst-xkey.tex 2005/11/25 v1.6 PSTricks specialization of xkeyval (HA) (/usr/share/texlive/texmf-dist/tex/latex/xkeyval/xkeyval.sty -Package: xkeyval 2014/05/25 v2.7 package option processing (HA) +Package: xkeyval 2012/10/14 v2.6b package option processing (HA) (/usr/share/texlive/texmf-dist/tex/generic/xkeyval/xkeyval.tex -(/usr/share/texlive/texmf-dist/tex/generic/xkeyval/xkvutils.tex \XKV@toks=\toks28 \XKV@tempa@toks=\toks29 -) \XKV@depth=\count114 -File: xkeyval.tex 2014/05/25 v2.7 key=value parser (HA) +File: xkeyval.tex 2012/10/14 v2.6b key=value parser (HA) ))) (/usr/share/texlive/texmf-dist/tex/generic/pstricks/pst-fp.tex `pst-fp' v0.05, 2010/01/17 (hv) @@ -593,125 +591,76 @@ File: xkeyval.tex 2014/05/25 v2.7 key=value parser (HA) \pstFP@regs=\count122 \pstFP@times=\count123 ) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfutil-common.tex +(/usr/share/texmf/tex/generic/pgf/utilities/pgfutil-common.tex \pgfutil@everybye=\toks30 -\pgfutil@tempdima=\dimen130 -\pgfutil@tempdimb=\dimen131 - -(/usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfutil-common-lists.t -ex)) (/usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfkeys.code.tex +) +(/usr/share/texmf/tex/generic/pgf/utilities/pgfkeys.code.tex \pgfkeys@pathtoks=\toks31 \pgfkeys@temptoks=\toks32 -(/usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfkeysfiltered.code.t -ex +(/usr/share/texmf/tex/generic/pgf/utilities/pgfkeysfiltered.code.tex \pgfkeys@tmptoks=\toks33 -)) (/usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgffor.code.tex -(/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmath.code.tex -(/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathcalc.code.tex -(/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathutil.code.tex -\pgf@x=\dimen132 -\pgf@xa=\dimen133 -\pgf@xb=\dimen134 -\pgf@xc=\dimen135 -\pgf@y=\dimen136 -\pgf@ya=\dimen137 -\pgf@yb=\dimen138 -\pgf@yc=\dimen139 -\c@pgf@counta=\count124 -\c@pgf@countb=\count125 -\c@pgf@countc=\count126 -\c@pgf@countd=\count127 -\pgfutil@tempcnta=\count128 -\pgfutil@tempcntb=\count129 -) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathparser.code.tex -\pgfmath@dimen=\dimen140 -\pgfmath@count=\count130 -\pgfmath@box=\box44 -\pgfmath@toks=\toks34 -\pgfmath@stack@operand=\toks35 -\pgfmath@stack@operation=\toks36 -) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.code.tex -(/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.basic.code -.tex) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.trigonomet -ric.code.tex) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.random.cod -e.tex) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.comparison -.code.tex) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.base.code. -tex) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.round.code -.tex) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.misc.code. -tex) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.integerari -thmetics.code.tex))) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfloat.code.tex -\c@pgfmathroundto@lastzeros=\count131 )) -\pgffor@iter=\dimen141 -\pgffor@skip=\dimen142 -\pgffor@stack=\toks37 -\pgffor@toks=\toks38 -) -\psLoopIndex=\count132 - -`PSTricks' v2.57 <2014/08/27> (tvz) -\pst@dima=\dimen143 -\pst@dimb=\dimen144 -\pst@dimc=\dimen145 -\pst@dimd=\dimen146 -\pst@dimg=\dimen147 -\pst@dimh=\dimen148 -\pst@dimm=\dimen149 -\pst@dimn=\dimen150 -\pst@dimo=\dimen151 -\pst@dimp=\dimen152 -\pst@hbox=\box45 -\pst@ibox=\box46 -\pst@boxg=\box47 -\pst@cnta=\count133 -\pst@cntb=\count134 -\pst@cntc=\count135 -\pst@cntd=\count136 -\pst@cntg=\count137 -\pst@cnth=\count138 -\pst@cntm=\count139 -\pst@cntn=\count140 -\pst@cnto=\count141 -\pst@cntp=\count142 -\@zero=\count143 -\pst@toks=\toks39 +(/usr/share/texmf/tex/generic/pgf/utilities/pgffor.code.tex +\pgffor@iter=\dimen130 +\pgffor@skip=\dimen131 +\pgffor@stack=\toks34 +\pgffor@toks=\toks35 +) +\psLoopIndex=\count124 + +`PSTricks' v2.51 <2014/02/03> (tvz) +\pst@dima=\dimen132 +\pst@dimb=\dimen133 +\pst@dimc=\dimen134 +\pst@dimd=\dimen135 +\pst@dimg=\dimen136 +\pst@dimh=\dimen137 +\pst@dimm=\dimen138 +\pst@dimn=\dimen139 +\pst@dimo=\dimen140 +\pst@dimp=\dimen141 +\pst@hbox=\box44 +\pst@ibox=\box45 +\pst@boxg=\box46 +\pst@cnta=\count125 +\pst@cntb=\count126 +\pst@cntc=\count127 +\pst@cntd=\count128 +\pst@cntg=\count129 +\pst@cnth=\count130 +\pst@cntm=\count131 +\pst@cntn=\count132 +\pst@cnto=\count133 +\pst@cntp=\count134 +\@zero=\count135 +\pst@toks=\toks36 (/usr/share/texlive/texmf-dist/tex/generic/pstricks/pstricks.con) -\psunit=\dimen153 -\psxunit=\dimen154 -\psyunit=\dimen155 -\pst@C@@rType=\count144 -\pslinewidth=\dimen156 -\psk@startLW=\dimen157 -\psk@endLW=\dimen158 -\pst@customdefs=\toks40 -\pslinearc=\dimen159 -\pst@symbolStep=\dimen160 -\pst@symbolWidth=\dimen161 -\pst@symbolLinewidth=\dimen162 -\everypsbox=\toks41 -\psframesep=\dimen163 -\pslabelsep=\dimen164 -\sh@wgridXunit=\dimen165 -\sh@wgridYunit=\dimen166 -\pst@shift=\dimen167 -) -File: pstricks.tex 2014/08/27 v2.57 `PSTricks' (tvz,hv) +\psunit=\dimen142 +\psxunit=\dimen143 +\psyunit=\dimen144 +\pst@C@@rType=\count136 +\pslinewidth=\dimen145 +\psk@startLW=\dimen146 +\psk@endLW=\dimen147 +\pst@customdefs=\toks37 +\pslinearc=\dimen148 +\pst@symbolStep=\dimen149 +\pst@symbolWidth=\dimen150 +\pst@symbolLinewidth=\dimen151 +\everypsbox=\toks38 +\psframesep=\dimen152 +\pslabelsep=\dimen153 +\sh@wgridXunit=\dimen154 +\sh@wgridYunit=\dimen155 +\pst@shift=\dimen156 +) +File: pstricks.tex 2014/02/03 v2.51 `PSTricks' (tvz,hv) (/usr/share/texlive/texmf-dist/tex/generic/pstricks/pst-fp.tex) -File: pst-fp.tex 2014/08/27 v2.57 `PST-fp' (hv) +File: pst-fp.tex 2014/02/03 v2.51 `PST-fp' (hv) -(/usr/share/texlive/texmf-dist/tex/latex/xcolor/xcolor.sty +(/usr/share/texmf/tex/latex/xcolor/xcolor.sty Package: xcolor 2007/01/21 v2.11 LaTeX color extensions (UK) (/usr/share/texlive/texmf-dist/tex/latex/latexconfig/color.cfg @@ -734,23 +683,23 @@ Package: pst-node 2012/09/18 v1.01 LaTeX wrapper for `pst-node' (HV) Package: pst-node 2010/04/22 package wrapper for pst-node.tex (/usr/share/texlive/texmf-dist/tex/generic/pst-node/pst-node.tex - v1.35, 2014/08/04 -\psrow=\count145 -\pscol=\count146 -\psmatrixcnt=\count147 + v1.32, 2014/02/03 +\psrow=\count137 +\pscol=\count138 +\psmatrixcnt=\count139 \psrowsep=\skip67 \pscolsep=\skip68 -\pst@args=\count148 -\num@pts=\count149 -\pst@argcnt=\count150 +\pst@args=\count140 +\num@pts=\count141 +\pst@argcnt=\count142 ) -File: pst-node.tex 2014/08/04 1.35 `pst-node' (tvz,hv) +File: pst-node.tex 2014/02/03 1.32 `pst-node' (tvz,hv) ) (/usr/share/texlive/texmf-dist/tex/latex/pst-coil/pst-coil.sty Package: pst-coil 2010/02/01 package wrapper for pst-coil.tex (hv) (/usr/share/texlive/texmf-dist/tex/generic/pst-coil/pst-coil.tex - v1.35, 2014/08/04 + v1.32, 2014/02/03 (/usr/share/texlive/texmf-dist/tex/generic/pst-node/pst-node.tex)) File: pst-coil.tex 2011/09/17 v1.06 `PST-coil' (tvz,hv) ) @@ -758,286 +707,275 @@ File: pst-coil.tex 2011/09/17 v1.06 `PST-coil' (tvz,hv) \Urlmuskip=\muskip11 Package: url 2013/09/16 ver 3.4 Verb mode for urls, etc. ) -(/usr/share/texlive/texmf-dist/tex/latex/pgf/frontendlayer/tikz.sty -(/usr/share/texlive/texmf-dist/tex/latex/pgf/basiclayer/pgf.sty -(/usr/share/texlive/texmf-dist/tex/latex/pgf/utilities/pgfrcs.sty -(/usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfutil-common.tex -\pgfutil@everybye=\toks42 -\pgfutil@tempdima=\dimen168 -\pgfutil@tempdimb=\dimen169 - -(/usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfutil-common-lists.t -ex)) (/usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfutil-latex.def -\pgfutil@abb=\box48 +(/usr/share/texmf/tex/latex/pgf/frontendlayer/tikz.sty +(/usr/share/texmf/tex/latex/pgf/basiclayer/pgf.sty +(/usr/share/texmf/tex/latex/pgf/utilities/pgfrcs.sty +(/usr/share/texmf/tex/generic/pgf/utilities/pgfutil-common.tex +\pgfutil@everybye=\toks39 +) +(/usr/share/texmf/tex/generic/pgf/utilities/pgfutil-latex.def +\pgfutil@abb=\box47 + (/usr/share/texlive/texmf-dist/tex/latex/ms/everyshi.sty Package: everyshi 2001/05/15 v3.00 EveryShipout Package (MS) )) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfrcs.code.tex -Package: pgfrcs 2013/12/20 v3.0.0 (rcs-revision 1.28) +(/usr/share/texmf/tex/generic/pgf/utilities/pgfrcs.code.tex +Package: pgfrcs 2010/10/25 v2.10 (rcs-revision 1.24) )) -Package: pgf 2013/12/18 v3.0.0 (rcs-revision 1.14) - -(/usr/share/texlive/texmf-dist/tex/latex/pgf/basiclayer/pgfcore.sty -(/usr/share/texlive/texmf-dist/tex/latex/pgf/systemlayer/pgfsys.sty -(/usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgfsys.code.tex -Package: pgfsys 2013/11/30 v3.0.0 (rcs-revision 1.47) - -(/usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfkeys.code.tex) -\pgf@x=\dimen170 -\pgf@y=\dimen171 -\pgf@xa=\dimen172 -\pgf@ya=\dimen173 -\pgf@xb=\dimen174 -\pgf@yb=\dimen175 -\pgf@xc=\dimen176 -\pgf@yc=\dimen177 +Package: pgf 2008/01/15 v2.10 (rcs-revision 1.12) + +(/usr/share/texmf/tex/latex/pgf/basiclayer/pgfcore.sty +(/usr/share/texmf/tex/latex/pgf/systemlayer/pgfsys.sty +(/usr/share/texmf/tex/generic/pgf/systemlayer/pgfsys.code.tex +Package: pgfsys 2010/06/30 v2.10 (rcs-revision 1.37) + +(/usr/share/texmf/tex/generic/pgf/utilities/pgfkeys.code.tex) +\pgf@x=\dimen157 +\pgf@y=\dimen158 +\pgf@xa=\dimen159 +\pgf@ya=\dimen160 +\pgf@xb=\dimen161 +\pgf@yb=\dimen162 +\pgf@xc=\dimen163 +\pgf@yc=\dimen164 \w@pgf@writea=\write3 \r@pgf@reada=\read1 -\c@pgf@counta=\count151 -\c@pgf@countb=\count152 -\c@pgf@countc=\count153 -\c@pgf@countd=\count154 -\t@pgf@toka=\toks43 -\t@pgf@tokb=\toks44 -\t@pgf@tokc=\toks45 - -(/usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgf.cfg +\c@pgf@counta=\count143 +\c@pgf@countb=\count144 +\c@pgf@countc=\count145 +\c@pgf@countd=\count146 + +(/usr/share/texmf/tex/generic/pgf/systemlayer/pgf.cfg File: pgf.cfg 2008/05/14 (rcs-revision 1.7) ) -Driver file for pgf: pgfsys-pdftex.def +Package pgfsys Info: Driver file for pgf: pgfsys-pdftex.def on input line 900. -(/usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgfsys-pdftex.def -File: pgfsys-pdftex.def 2013/07/18 (rcs-revision 1.33) +(/usr/share/texmf/tex/generic/pgf/systemlayer/pgfsys-pdftex.def +File: pgfsys-pdftex.def 2009/05/22 (rcs-revision 1.26) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgfsys-common-pdf.de -f -File: pgfsys-common-pdf.def 2013/10/10 (rcs-revision 1.13) +(/usr/share/texmf/tex/generic/pgf/systemlayer/pgfsys-common-pdf.def +File: pgfsys-common-pdf.def 2008/05/19 (rcs-revision 1.10) ))) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgfsyssoftpath.code. -tex -File: pgfsyssoftpath.code.tex 2013/09/09 (rcs-revision 1.9) -\pgfsyssoftpath@smallbuffer@items=\count155 -\pgfsyssoftpath@bigbuffer@items=\count156 -) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgfsysprotocol.code. -tex +(/usr/share/texmf/tex/generic/pgf/systemlayer/pgfsyssoftpath.code.tex +File: pgfsyssoftpath.code.tex 2008/07/18 (rcs-revision 1.7) +\pgfsyssoftpath@smallbuffer@items=\count147 +\pgfsyssoftpath@bigbuffer@items=\count148 +) +(/usr/share/texmf/tex/generic/pgf/systemlayer/pgfsysprotocol.code.tex File: pgfsysprotocol.code.tex 2006/10/16 (rcs-revision 1.4) )) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcore.code.tex -Package: pgfcore 2010/04/11 v3.0.0 (rcs-revision 1.7) - -(/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmath.code.tex) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepoints.code.te -x -File: pgfcorepoints.code.tex 2013/10/07 (rcs-revision 1.27) -\pgf@picminx=\dimen178 -\pgf@picmaxx=\dimen179 -\pgf@picminy=\dimen180 -\pgf@picmaxy=\dimen181 -\pgf@pathminx=\dimen182 -\pgf@pathmaxx=\dimen183 -\pgf@pathminy=\dimen184 -\pgf@pathmaxy=\dimen185 -\pgf@xx=\dimen186 -\pgf@xy=\dimen187 -\pgf@yx=\dimen188 -\pgf@yy=\dimen189 -\pgf@zx=\dimen190 -\pgf@zy=\dimen191 -) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepathconstruct. -code.tex -File: pgfcorepathconstruct.code.tex 2013/10/07 (rcs-revision 1.29) -\pgf@path@lastx=\dimen192 -\pgf@path@lasty=\dimen193 -) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepathusage.code -.tex -File: pgfcorepathusage.code.tex 2013/12/13 (rcs-revision 1.23) -\pgf@shorten@end@additional=\dimen194 -\pgf@shorten@start@additional=\dimen195 -) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorescopes.code.te -x -File: pgfcorescopes.code.tex 2013/10/09 (rcs-revision 1.44) +(/usr/share/texmf/tex/generic/pgf/basiclayer/pgfcore.code.tex +Package: pgfcore 2010/04/11 v2.10 (rcs-revision 1.7) + +(/usr/share/texmf/tex/generic/pgf/math/pgfmath.code.tex +(/usr/share/texmf/tex/generic/pgf/math/pgfmathcalc.code.tex +(/usr/share/texmf/tex/generic/pgf/math/pgfmathutil.code.tex) +(/usr/share/texmf/tex/generic/pgf/math/pgfmathparser.code.tex +\pgfmath@dimen=\dimen165 +\pgfmath@count=\count149 +\pgfmath@box=\box48 +\pgfmath@toks=\toks40 +\pgfmath@stack@operand=\toks41 +\pgfmath@stack@operation=\toks42 +) +(/usr/share/texmf/tex/generic/pgf/math/pgfmathfunctions.code.tex +(/usr/share/texmf/tex/generic/pgf/math/pgfmathfunctions.basic.code.tex) +(/usr/share/texmf/tex/generic/pgf/math/pgfmathfunctions.trigonometric.code.tex) +(/usr/share/texmf/tex/generic/pgf/math/pgfmathfunctions.random.code.tex) +(/usr/share/texmf/tex/generic/pgf/math/pgfmathfunctions.comparison.code.tex) +(/usr/share/texmf/tex/generic/pgf/math/pgfmathfunctions.base.code.tex) +(/usr/share/texmf/tex/generic/pgf/math/pgfmathfunctions.round.code.tex) +(/usr/share/texmf/tex/generic/pgf/math/pgfmathfunctions.misc.code.tex))) +(/usr/share/texmf/tex/generic/pgf/math/pgfmathfloat.code.tex +\c@pgfmathroundto@lastzeros=\count150 +)) +(/usr/share/texmf/tex/generic/pgf/basiclayer/pgfcorepoints.code.tex +File: pgfcorepoints.code.tex 2010/04/09 (rcs-revision 1.20) +\pgf@picminx=\dimen166 +\pgf@picmaxx=\dimen167 +\pgf@picminy=\dimen168 +\pgf@picmaxy=\dimen169 +\pgf@pathminx=\dimen170 +\pgf@pathmaxx=\dimen171 +\pgf@pathminy=\dimen172 +\pgf@pathmaxy=\dimen173 +\pgf@xx=\dimen174 +\pgf@xy=\dimen175 +\pgf@yx=\dimen176 +\pgf@yy=\dimen177 +\pgf@zx=\dimen178 +\pgf@zy=\dimen179 +) +(/usr/share/texmf/tex/generic/pgf/basiclayer/pgfcorepathconstruct.code.tex +File: pgfcorepathconstruct.code.tex 2010/08/03 (rcs-revision 1.24) +\pgf@path@lastx=\dimen180 +\pgf@path@lasty=\dimen181 +) +(/usr/share/texmf/tex/generic/pgf/basiclayer/pgfcorepathusage.code.tex +File: pgfcorepathusage.code.tex 2008/04/22 (rcs-revision 1.12) +\pgf@shorten@end@additional=\dimen182 +\pgf@shorten@start@additional=\dimen183 +) +(/usr/share/texmf/tex/generic/pgf/basiclayer/pgfcorescopes.code.tex +File: pgfcorescopes.code.tex 2010/09/08 (rcs-revision 1.34) \pgfpic=\box49 \pgf@hbox=\box50 \pgf@layerbox@main=\box51 -\pgf@picture@serial@count=\count157 +\pgf@picture@serial@count=\count151 ) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoregraphicstate.c -ode.tex -File: pgfcoregraphicstate.code.tex 2013/09/19 (rcs-revision 1.11) -\pgflinewidth=\dimen196 +(/usr/share/texmf/tex/generic/pgf/basiclayer/pgfcoregraphicstate.code.tex +File: pgfcoregraphicstate.code.tex 2008/04/22 (rcs-revision 1.9) +\pgflinewidth=\dimen184 ) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoretransformation -s.code.tex -File: pgfcoretransformations.code.tex 2013/10/10 (rcs-revision 1.17) -\pgf@pt@x=\dimen197 -\pgf@pt@y=\dimen198 -\pgf@pt@temp=\dimen199 +(/usr/share/texmf/tex/generic/pgf/basiclayer/pgfcoretransformations.code.tex +File: pgfcoretransformations.code.tex 2009/06/10 (rcs-revision 1.11) +\pgf@pt@x=\dimen185 +\pgf@pt@y=\dimen186 +\pgf@pt@temp=\dimen187 ) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorequick.code.tex +(/usr/share/texmf/tex/generic/pgf/basiclayer/pgfcorequick.code.tex File: pgfcorequick.code.tex 2008/10/09 (rcs-revision 1.3) ) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreobjects.code.t -ex +(/usr/share/texmf/tex/generic/pgf/basiclayer/pgfcoreobjects.code.tex File: pgfcoreobjects.code.tex 2006/10/11 (rcs-revision 1.2) ) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepathprocessing -.code.tex -File: pgfcorepathprocessing.code.tex 2013/09/09 (rcs-revision 1.9) +(/usr/share/texmf/tex/generic/pgf/basiclayer/pgfcorepathprocessing.code.tex +File: pgfcorepathprocessing.code.tex 2008/10/09 (rcs-revision 1.8) ) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorearrows.code.te -x -File: pgfcorearrows.code.tex 2013/11/07 (rcs-revision 1.40) -\pgfarrowsep=\dimen200 +(/usr/share/texmf/tex/generic/pgf/basiclayer/pgfcorearrows.code.tex +File: pgfcorearrows.code.tex 2008/04/23 (rcs-revision 1.11) ) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreshade.code.tex -File: pgfcoreshade.code.tex 2013/07/15 (rcs-revision 1.15) -\pgf@max=\dimen201 -\pgf@sys@shading@range@num=\count158 +(/usr/share/texmf/tex/generic/pgf/basiclayer/pgfcoreshade.code.tex +File: pgfcoreshade.code.tex 2008/11/23 (rcs-revision 1.13) +\pgf@max=\dimen188 +\pgf@sys@shading@range@num=\count152 ) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreimage.code.tex -File: pgfcoreimage.code.tex 2013/07/15 (rcs-revision 1.18) +(/usr/share/texmf/tex/generic/pgf/basiclayer/pgfcoreimage.code.tex +File: pgfcoreimage.code.tex 2010/03/25 (rcs-revision 1.16) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreexternal.code. -tex -File: pgfcoreexternal.code.tex 2013/07/15 (rcs-revision 1.20) +(/usr/share/texmf/tex/generic/pgf/basiclayer/pgfcoreexternal.code.tex +File: pgfcoreexternal.code.tex 2010/09/01 (rcs-revision 1.17) \pgfexternal@startupbox=\box52 )) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorelayers.code.te -x -File: pgfcorelayers.code.tex 2013/07/18 (rcs-revision 1.7) +(/usr/share/texmf/tex/generic/pgf/basiclayer/pgfcorelayers.code.tex +File: pgfcorelayers.code.tex 2010/08/27 (rcs-revision 1.2) ) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoretransparency.c -ode.tex -File: pgfcoretransparency.code.tex 2013/09/30 (rcs-revision 1.5) +(/usr/share/texmf/tex/generic/pgf/basiclayer/pgfcoretransparency.code.tex +File: pgfcoretransparency.code.tex 2008/01/17 (rcs-revision 1.2) ) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepatterns.code. -tex -File: pgfcorepatterns.code.tex 2013/11/07 (rcs-revision 1.5) +(/usr/share/texmf/tex/generic/pgf/basiclayer/pgfcorepatterns.code.tex +File: pgfcorepatterns.code.tex 2009/07/02 (rcs-revision 1.3) ))) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/modules/pgfmoduleshapes.code.tex -File: pgfmoduleshapes.code.tex 2013/10/31 (rcs-revision 1.34) +(/usr/share/texmf/tex/generic/pgf/modules/pgfmoduleshapes.code.tex +File: pgfmoduleshapes.code.tex 2010/09/09 (rcs-revision 1.13) \pgfnodeparttextbox=\box53 -) (/usr/share/texlive/texmf-dist/tex/generic/pgf/modules/pgfmoduleplot.code.tex -File: pgfmoduleplot.code.tex 2013/07/31 (rcs-revision 1.12) -) -(/usr/share/texlive/texmf-dist/tex/latex/pgf/compatibility/pgfcomp-version-0-65 -.sty -Package: pgfcomp-version-0-65 2007/07/03 v3.0.0 (rcs-revision 1.7) -\pgf@nodesepstart=\dimen202 -\pgf@nodesepend=\dimen203 -) -(/usr/share/texlive/texmf-dist/tex/latex/pgf/compatibility/pgfcomp-version-1-18 -.sty -Package: pgfcomp-version-1-18 2007/07/23 v3.0.0 (rcs-revision 1.1) -)) (/usr/share/texlive/texmf-dist/tex/latex/pgf/utilities/pgffor.sty -(/usr/share/texlive/texmf-dist/tex/latex/pgf/utilities/pgfkeys.sty -(/usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfkeys.code.tex)) -(/usr/share/texlive/texmf-dist/tex/latex/pgf/math/pgfmath.sty -(/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmath.code.tex)) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgffor.code.tex -Package: pgffor 2013/12/13 v3.0.0 (rcs-revision 1.25) - -(/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmath.code.tex) -\pgffor@iter=\dimen204 -\pgffor@skip=\dimen205 -\pgffor@stack=\toks46 -\pgffor@toks=\toks47 +) +(/usr/share/texmf/tex/generic/pgf/modules/pgfmoduleplot.code.tex +File: pgfmoduleplot.code.tex 2010/10/22 (rcs-revision 1.8) +) +(/usr/share/texmf/tex/latex/pgf/compatibility/pgfcomp-version-0-65.sty +Package: pgfcomp-version-0-65 2007/07/03 v2.10 (rcs-revision 1.7) +\pgf@nodesepstart=\dimen189 +\pgf@nodesepend=\dimen190 +) +(/usr/share/texmf/tex/latex/pgf/compatibility/pgfcomp-version-1-18.sty +Package: pgfcomp-version-1-18 2007/07/23 v2.10 (rcs-revision 1.1) +)) +(/usr/share/texmf/tex/latex/pgf/utilities/pgffor.sty +(/usr/share/texmf/tex/latex/pgf/utilities/pgfkeys.sty +(/usr/share/texmf/tex/generic/pgf/utilities/pgfkeys.code.tex)) +(/usr/share/texmf/tex/generic/pgf/utilities/pgffor.code.tex +Package: pgffor 2010/03/23 v2.10 (rcs-revision 1.18) +\pgffor@iter=\dimen191 +\pgffor@skip=\dimen192 +\pgffor@stack=\toks43 +\pgffor@toks=\toks44 )) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/tikz.code.tex -Package: tikz 2013/12/13 v3.0.0 (rcs-revision 1.142) - -(/usr/share/texlive/texmf-dist/tex/generic/pgf/libraries/pgflibraryplothandlers -.code.tex -File: pgflibraryplothandlers.code.tex 2013/08/31 v3.0.0 (rcs-revision 1.20) -\pgf@plot@mark@count=\count159 -\pgfplotmarksize=\dimen206 -) -\tikz@lastx=\dimen207 -\tikz@lasty=\dimen208 -\tikz@lastxsaved=\dimen209 -\tikz@lastysaved=\dimen210 -\tikzleveldistance=\dimen211 -\tikzsiblingdistance=\dimen212 +(/usr/share/texmf/tex/generic/pgf/frontendlayer/tikz/tikz.code.tex +Package: tikz 2010/10/13 v2.10 (rcs-revision 1.76) + +(/usr/share/texmf/tex/generic/pgf/libraries/pgflibraryplothandlers.code.tex +File: pgflibraryplothandlers.code.tex 2010/05/31 v2.10 (rcs-revision 1.15) +\pgf@plot@mark@count=\count153 +\pgfplotmarksize=\dimen193 +) +\tikz@lastx=\dimen194 +\tikz@lasty=\dimen195 +\tikz@lastxsaved=\dimen196 +\tikz@lastysaved=\dimen197 +\tikzleveldistance=\dimen198 +\tikzsiblingdistance=\dimen199 \tikz@figbox=\box54 -\tikz@figbox@bg=\box55 -\tikz@tempbox=\box56 -\tikz@tempbox@bg=\box57 -\tikztreelevel=\count160 -\tikznumberofchildren=\count161 -\tikznumberofcurrentchild=\count162 -\tikz@fig@count=\count163 - -(/usr/share/texlive/texmf-dist/tex/generic/pgf/modules/pgfmodulematrix.code.tex -File: pgfmodulematrix.code.tex 2013/09/17 (rcs-revision 1.8) -\pgfmatrixcurrentrow=\count164 -\pgfmatrixcurrentcolumn=\count165 -\pgf@matrix@numberofcolumns=\count166 -) -\tikz@expandcount=\count167 - -(/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tik -zlibrarytopaths.code.tex -File: tikzlibrarytopaths.code.tex 2008/06/17 v3.0.0 (rcs-revision 1.2) +\tikz@tempbox=\box55 +\tikztreelevel=\count154 +\tikznumberofchildren=\count155 +\tikznumberofcurrentchild=\count156 +\tikz@fig@count=\count157 + +(/usr/share/texmf/tex/generic/pgf/modules/pgfmodulematrix.code.tex +File: pgfmodulematrix.code.tex 2010/08/24 (rcs-revision 1.4) +\pgfmatrixcurrentrow=\count158 +\pgfmatrixcurrentcolumn=\count159 +\pgf@matrix@numberofcolumns=\count160 +) +\tikz@expandcount=\count161 + +(/usr/share/texmf/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarytopat +hs.code.tex +File: tikzlibrarytopaths.code.tex 2008/06/17 v2.10 (rcs-revision 1.2) ))) -(/usr/share/texlive/texmf-dist/tex/latex/pgf/compatibility/pgflibrarysnakes.sty +(/usr/share/texmf/tex/latex/pgf/compatibility/pgflibrarysnakes.sty Package pgf Warning: This package is obsolete. Use \usetikzlibrary {snakes} ins tead on input line 11. - -(/usr/share/texlive/texmf-dist/tex/generic/pgf/libraries/pgflibrarysnakes.code. -tex -File: pgflibrarysnakes.code.tex 2013/07/15 v3.0.0 (rcs-revision 1.25) +(/usr/share/texmf/tex/generic/pgf/libraries/pgflibrarysnakes.code.tex +File: pgflibrarysnakes.code.tex 2008/01/19 v2.10 (rcs-revision 1.24) Package pgf Warning: Snakes have been superseded by decorations. Use the decora -tion libraries instead of the snakes library on input line 12. - - -(/usr/share/texlive/texmf-dist/tex/generic/pgf/libraries/decorations/pgflibrary -decorations.pathmorphing.code.tex -(/usr/share/texlive/texmf-dist/tex/generic/pgf/modules/pgfmoduledecorations.cod -e.tex -\pgfdecoratedcompleteddistance=\dimen213 -\pgfdecoratedremainingdistance=\dimen214 -\pgfdecoratedinputsegmentcompleteddistance=\dimen215 -\pgfdecoratedinputsegmentremainingdistance=\dimen216 -\pgf@decorate@distancetomove=\dimen217 -\pgf@decorate@repeatstate=\count168 -\pgfdecorationsegmentamplitude=\dimen218 -\pgfdecorationsegmentlength=\dimen219 +tion libraries instead of the snakes library on input line 13. + + +(/usr/share/texmf/tex/generic/pgf/libraries/decorations/pgflibrarydecorations.p +athmorphing.code.tex +(/usr/share/texmf/tex/generic/pgf/modules/pgfmoduledecorations.code.tex +\pgfdecoratedcompleteddistance=\dimen200 +\pgfdecoratedremainingdistance=\dimen201 +\pgfdecoratedinputsegmentcompleteddistance=\dimen202 +\pgfdecoratedinputsegmentremainingdistance=\dimen203 +\pgf@decorate@distancetomove=\dimen204 +\pgf@decorate@repeatstate=\count162 +\pgfdecorationsegmentamplitude=\dimen205 +\pgfdecorationsegmentlength=\dimen206 )) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/libraries/decorations/pgflibrary -decorations.pathreplacing.code.tex) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/libraries/decorations/pgflibrary -decorations.shapes.code.tex))) -(/usr/share/texlive/texmf-dist/tex/latex/tools/multicol.sty -Package: multicol 2014/10/28 v1.8i multicolumn formatting (FMi) -\c@tracingmulticols=\count169 -\mult@box=\box58 -\multicol@leftmargin=\dimen220 -\c@unbalance=\count170 -\c@collectmore=\count171 -\doublecol@number=\count172 -\multicoltolerance=\count173 -\multicolpretolerance=\count174 -\full@width=\dimen221 -\page@free=\dimen222 -\premulticols=\dimen223 -\postmulticols=\dimen224 +(/usr/share/texmf/tex/generic/pgf/libraries/decorations/pgflibrarydecorations.p +athreplacing.code.tex) +(/usr/share/texmf/tex/generic/pgf/libraries/decorations/pgflibrarydecorations.s +hapes.code.tex))) (/usr/share/texlive/texmf-dist/tex/latex/tools/multicol.sty +Package: multicol 2011/06/27 v1.7a multicolumn formatting (FMi) +\c@tracingmulticols=\count163 +\mult@box=\box56 +\multicol@leftmargin=\dimen207 +\c@unbalance=\count164 +\c@collectmore=\count165 +\doublecol@number=\count166 +\multicoltolerance=\count167 +\multicolpretolerance=\count168 +\full@width=\dimen208 +\page@free=\dimen209 +\premulticols=\dimen210 +\postmulticols=\dimen211 \multicolsep=\skip69 \multicolbaselineskip=\skip70 -\partial@page=\box59 -\last@line=\box60 -\maxbalancingoverflow=\dimen225 -\mult@rightbox=\box61 -\mult@grightbox=\box62 -\mult@gfirstbox=\box63 -\mult@firstbox=\box64 +\partial@page=\box57 +\last@line=\box58 +\mult@rightbox=\box59 +\mult@grightbox=\box60 +\mult@gfirstbox=\box61 +\mult@firstbox=\box62 +\@tempa=\box63 +\@tempa=\box64 \@tempa=\box65 \@tempa=\box66 \@tempa=\box67 @@ -1053,119 +991,114 @@ Package: multicol 2014/10/28 v1.8i multicolumn formatting (FMi) \@tempa=\box77 \@tempa=\box78 \@tempa=\box79 -\@tempa=\box80 -\@tempa=\box81 -\c@columnbadness=\count175 -\c@finalcolumnbadness=\count176 -\last@try=\dimen226 -\multicolovershoot=\dimen227 -\multicolundershoot=\dimen228 -\mult@nat@firstbox=\box82 -\colbreak@box=\box83 -\mc@col@check@num=\count177 -) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tik -zlibraryarrows.code.tex -File: tikzlibraryarrows.code.tex 2008/01/09 v3.0.0 (rcs-revision 1.1) - -(/usr/share/texlive/texmf-dist/tex/generic/pgf/libraries/pgflibraryarrows.code. -tex -File: pgflibraryarrows.code.tex 2013/09/23 v3.0.0 (rcs-revision 1.16) -\arrowsize=\dimen229 -)) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tik -zlibraryautomata.code.tex -File: tikzlibraryautomata.code.tex 2008/07/14 v3.0.0 (rcs-revision 1.3) - -(/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tik -zlibraryshapes.multipart.code.tex -File: tikzlibraryshapes.multipart.code.tex 2008/01/09 v3.0.0 (rcs-revision 1.1) +\c@columnbadness=\count169 +\c@finalcolumnbadness=\count170 +\last@try=\dimen212 +\multicolovershoot=\dimen213 +\multicolundershoot=\dimen214 +\mult@nat@firstbox=\box80 +\colbreak@box=\box81 +\multicol@sort@counter=\count171 +) +(/usr/share/texmf/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryarrow +s.code.tex +File: tikzlibraryarrows.code.tex 2008/01/09 v2.10 (rcs-revision 1.1) +(/usr/share/texmf/tex/generic/pgf/libraries/pgflibraryarrows.code.tex +File: pgflibraryarrows.code.tex 2008/10/27 v2.10 (rcs-revision 1.9) +\arrowsize=\dimen215 +)) +(/usr/share/texmf/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryautom +ata.code.tex +File: tikzlibraryautomata.code.tex 2008/07/14 v2.10 (rcs-revision 1.3) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/libraries/shapes/pgflibraryshape +(/usr/share/texmf/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshape s.multipart.code.tex -File: pgflibraryshapes.multipart.code.tex 2010/01/07 v3.0.0 (rcs-revision 1.2) -\pgfnodepartlowerbox=\box84 -\pgfnodeparttwobox=\box85 -\pgfnodepartthreebox=\box86 -\pgfnodepartfourbox=\box87 -\pgfnodeparttwentybox=\box88 -\pgfnodepartnineteenbox=\box89 -\pgfnodeparteighteenbox=\box90 -\pgfnodepartseventeenbox=\box91 -\pgfnodepartsixteenbox=\box92 -\pgfnodepartfifteenbox=\box93 -\pgfnodepartfourteenbox=\box94 -\pgfnodepartthirteenbox=\box95 -\pgfnodeparttwelvebox=\box96 -\pgfnodepartelevenbox=\box97 -\pgfnodeparttenbox=\box98 -\pgfnodepartninebox=\box99 -\pgfnodeparteightbox=\box100 -\pgfnodepartsevenbox=\box101 -\pgfnodepartsixbox=\box102 -\pgfnodepartfivebox=\box103 +File: tikzlibraryshapes.multipart.code.tex 2008/01/09 v2.10 (rcs-revision 1.1) + +(/usr/share/texmf/tex/generic/pgf/libraries/shapes/pgflibraryshapes.multipart.c +ode.tex +File: pgflibraryshapes.multipart.code.tex 2010/01/07 v2.10 (rcs-revision 1.2) +\pgfnodepartlowerbox=\box82 +\pgfnodeparttwobox=\box83 +\pgfnodepartthreebox=\box84 +\pgfnodepartfourbox=\box85 +\pgfnodeparttwentybox=\box86 +\pgfnodepartnineteenbox=\box87 +\pgfnodeparteighteenbox=\box88 +\pgfnodepartseventeenbox=\box89 +\pgfnodepartsixteenbox=\box90 +\pgfnodepartfifteenbox=\box91 +\pgfnodepartfourteenbox=\box92 +\pgfnodepartthirteenbox=\box93 +\pgfnodeparttwelvebox=\box94 +\pgfnodepartelevenbox=\box95 +\pgfnodeparttenbox=\box96 +\pgfnodepartninebox=\box97 +\pgfnodeparteightbox=\box98 +\pgfnodepartsevenbox=\box99 +\pgfnodepartsixbox=\box100 +\pgfnodepartfivebox=\box101 ))) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tik -zlibrarysnakes.code.tex -File: tikzlibrarysnakes.code.tex 2013/07/15 v3.0.0 (rcs-revision 1.7) +(/usr/share/texmf/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarysnake +s.code.tex +File: tikzlibrarysnakes.code.tex 2008/02/05 v2.10 (rcs-revision 1.6) -Package pgf Warning: Snakes have been superseded by decorations. Please use the - decoration libraries instead of the snakes library on input line 14. +Package tikz Warning: Snakes have been superseded by decorations. Please use th +e decoration libraries instead of the snakes library on input line 14. -(/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tik -zlibrarydecorations.pathmorphing.code.tex -(/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tik -zlibrarydecorations.code.tex -\tikz@lib@dec@box=\box104 +(/usr/share/texmf/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecor +ations.pathmorphing.code.tex +(/usr/share/texmf/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecor +ations.code.tex +\tikz@lib@dec@box=\box102 )) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tik -zlibrarydecorations.pathreplacing.code.tex) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tik -zlibrarydecorations.shapes.code.tex)) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tik -zlibraryshapes.code.tex -File: tikzlibraryshapes.code.tex 2008/01/09 v3.0.0 (rcs-revision 1.1) - -(/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tik -zlibraryshapes.geometric.code.tex -File: tikzlibraryshapes.geometric.code.tex 2008/01/09 v3.0.0 (rcs-revision 1.1) - +(/usr/share/texmf/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecor +ations.pathreplacing.code.tex) +(/usr/share/texmf/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecor +ations.shapes.code.tex)) +(/usr/share/texmf/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshape +s.code.tex +File: tikzlibraryshapes.code.tex 2008/01/09 v2.10 (rcs-revision 1.1) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/libraries/shapes/pgflibraryshape +(/usr/share/texmf/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshape s.geometric.code.tex -File: pgflibraryshapes.geometric.code.tex 2008/06/26 v3.0.0 (rcs-revision 1.1) -)) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tik -zlibraryshapes.misc.code.tex -File: tikzlibraryshapes.misc.code.tex 2008/01/09 v3.0.0 (rcs-revision 1.1) +File: tikzlibraryshapes.geometric.code.tex 2008/01/09 v2.10 (rcs-revision 1.1) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/libraries/shapes/pgflibraryshape -s.misc.code.tex -File: pgflibraryshapes.misc.code.tex 2013/07/18 v3.0.0 (rcs-revision 1.5) +(/usr/share/texmf/tex/generic/pgf/libraries/shapes/pgflibraryshapes.geometric.c +ode.tex +File: pgflibraryshapes.geometric.code.tex 2008/06/26 v2.10 (rcs-revision 1.1) )) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tik -zlibraryshapes.symbols.code.tex -File: tikzlibraryshapes.symbols.code.tex 2008/01/09 v3.0.0 (rcs-revision 1.1) +(/usr/share/texmf/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshape +s.misc.code.tex +File: tikzlibraryshapes.misc.code.tex 2008/01/09 v2.10 (rcs-revision 1.1) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/libraries/shapes/pgflibraryshape -s.symbols.code.tex -File: pgflibraryshapes.symbols.code.tex 2013/09/11 v3.0.0 (rcs-revision 1.6) +(/usr/share/texmf/tex/generic/pgf/libraries/shapes/pgflibraryshapes.misc.code.t +ex +File: pgflibraryshapes.misc.code.tex 2008/10/07 v2.10 (rcs-revision 1.3) )) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tik -zlibraryshapes.arrows.code.tex -File: tikzlibraryshapes.arrows.code.tex 2008/01/09 v3.0.0 (rcs-revision 1.1) +(/usr/share/texmf/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshape +s.symbols.code.tex +File: tikzlibraryshapes.symbols.code.tex 2008/01/09 v2.10 (rcs-revision 1.1) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/libraries/shapes/pgflibraryshape +(/usr/share/texmf/tex/generic/pgf/libraries/shapes/pgflibraryshapes.symbols.cod +e.tex +File: pgflibraryshapes.symbols.code.tex 2009/10/27 v2.10 (rcs-revision 1.3) +)) +(/usr/share/texmf/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshape s.arrows.code.tex -File: pgflibraryshapes.arrows.code.tex 2008/06/26 v3.0.0 (rcs-revision 1.1) +File: tikzlibraryshapes.arrows.code.tex 2008/01/09 v2.10 (rcs-revision 1.1) + +(/usr/share/texmf/tex/generic/pgf/libraries/shapes/pgflibraryshapes.arrows.code +.tex +File: pgflibraryshapes.arrows.code.tex 2008/06/26 v2.10 (rcs-revision 1.1) )) -(/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tik -zlibraryshapes.callouts.code.tex -(/usr/share/texlive/texmf-dist/tex/generic/pgf/libraries/shapes/pgflibraryshape -s.callouts.code.tex))) (./main.aux) +(/usr/share/texmf/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshape +s.callouts.code.tex +(/usr/share/texmf/tex/generic/pgf/libraries/shapes/pgflibraryshapes.callouts.co +de.tex))) (./main.aux) \openout1 = `main.aux'. LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 87. @@ -1200,54 +1133,25 @@ File: ulasy.fd 1998/08/17 v2.2e LaTeX symbol font definitions ) (/usr/share/texlive/texmf-dist/tex/context/base/supp-pdf.mkii [Loading MPS to PDF converter (version 2006.09.02).] -\scratchcounter=\count178 -\scratchdimen=\dimen230 -\scratchbox=\box105 -\nofMPsegments=\count179 -\nofMParguments=\count180 -\everyMPshowfont=\toks48 -\MPscratchCnt=\count181 -\MPscratchDim=\dimen231 -\MPnumerator=\count182 -\makeMPintoPDFobject=\count183 -\everyMPtoPDFconversion=\toks49 +\scratchcounter=\count172 +\scratchdimen=\dimen216 +\scratchbox=\box103 +\nofMPsegments=\count173 +\nofMParguments=\count174 +\everyMPshowfont=\toks45 +\MPscratchCnt=\count175 +\MPscratchDim=\dimen217 +\MPnumerator=\count176 +\makeMPintoPDFobject=\count177 +\everyMPtoPDFconversion=\toks46 ) Package caption Info: Begin \AtBeginDocument code. Package caption Info: End \AtBeginDocument code. ABD: EveryShipout initializing macros (./intro.tex - -LaTeX Warning: Citation `915396' on page 1 undefined on input line 2. - - -LaTeX Warning: Citation `915385' on page 1 undefined on input line 2. - - -LaTeX Warning: Citation `5376454' on page 1 undefined on input line 2. - - -LaTeX Warning: Citation `915396' on page 1 undefined on input line 5. - - -LaTeX Warning: Citation `915385' on page 1 undefined on input line 5. - - -LaTeX Warning: Citation `5376454' on page 1 undefined on input line 5. - - -LaTeX Warning: Citation `Marsaglia1996' on page 1 undefined on input line 10. - - -LaTeX Warning: Citation `Nist10' on page 1 undefined on input line 10. - - -LaTeX Warning: Citation `LEcuyerS07' on page 1 undefined on input line 10. - - -LaTeX Warning: Citation `Devaney' on page 1 undefined on input line 19. - LaTeX Font Info: Try loading font information for OMS+cmr on input line 26. + (/usr/share/texlive/texmf-dist/tex/latex/base/omscmr.fd -File: omscmr.fd 2014/09/29 v2.5h Standard LaTeX font definitions +File: omscmr.fd 1999/05/25 v2.5h Standard LaTeX font definitions ) LaTeX Font Info: Font shape `OMS/cmr/m/n' in size <7> not available (Font) Font shape `OMS/cmsy/m/n' tried instead on input line 26. @@ -1261,35 +1165,7 @@ Non-PDF special ignored! Non-PDF special ignored! Non-PDF special ignored! Non-PDF special ignored! -Non-PDF special ignored!{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}] - -LaTeX Warning: Citation `guyeuxTaiwan10' on page 2 undefined on input line 31. - - -LaTeX Warning: Citation `bcgr11:ip' on page 2 undefined on input line 31. - - -LaTeX Warning: Citation `wbg10ip' on page 2 undefined on input line 32. - - -LaTeX Warning: Citation `chgw14oip' on page 2 undefined on input line 33. - - -LaTeX Warning: Citation `bcgr11:ip' on page 2 undefined on input line 35. - - -LaTeX Warning: Citation `chgw14oip' on page 2 undefined on input line 42. - - -LaTeX Warning: Citation `chgw14oip' on page 2 undefined on input line 58. - - -LaTeX Warning: Reference `sec:hypercube' on page 2 undefined on input line 96. - - -LaTeX Warning: Reference `sec:prng' on page 2 undefined on input line 100. - -) +Non-PDF special ignored!{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}]) Underfull \vbox (badness 10000) has occurred while \output is active [] [2] @@ -1305,25 +1181,7 @@ File: images/iter_f0c.pdf Graphic file (type pdf) Package pdftex.def Info: images/iter_f0c.pdf used on input line 60. (pdftex.def) Requested size: 230.36006pt x 170.13521pt. - - -LaTeX Warning: Citation `DBLP:conf/secrypt/CouchotHGWB14' on page 3 undefined o -n input line 66. - -) [3] (./chaos.tex - -LaTeX Warning: Citation `bcgr11:ip' on page 4 undefined on input line 2. - - -LaTeX Warning: Citation `bcgr11:ip' on page 4 undefined on input line 21. - -[4 <./images/iter_f0c.pdf>] - -LaTeX Warning: Citation `Devaney' on page 5 undefined on input line 62. - - -LaTeX Warning: Citation `Banks92' on page 5 undefined on input line 79. - + [3]) (./chaos.tex [4 <./images/iter_f0c.pdf>] [5] Overfull \hbox (12.18526pt too wide) in paragraph at lines 229--232 []\T1/cmr/m/n/10 The next $\OML/cmm/m/it/10 n \OMS/cmsy/m/n/10 ^^B [] []$ \T1/c @@ -1376,86 +1234,8 @@ Underfull \hbox (badness 10000) in paragraph at lines 472--477 ; :::; a[]; :::; a[];$ [] -[9 <./graphe1.pdf> <./graphe2.pdf>]) (./generating.tex - -LaTeX Warning: Citation `bcgr11:ip' on page 10 undefined on input line 2. - - -LaTeX Warning: Citation `DBLP:conf/secrypt/CouchotHGWB14' on page 10 undefined -on input line 9. - -[10] - -LaTeX Warning: Citation `bcgr11:ip' on page 11 undefined on input line 61. - -) (./hamilton.tex - -LaTeX Warning: Citation `Robinson:1981:CS' on page 11 undefined on input line 2 -. - - -LaTeX Warning: Citation `DBLP:journals/combinatorics/BhatS96' on page 11 undefi -ned on input line 2. - - -LaTeX Warning: Citation `ZanSup04' on page 11 undefined on input line 2. - - -LaTeX Warning: Citation `Bykov2016' on page 11 undefined on input line 2. - - -LaTeX Warning: Citation `DBLP:journals/combinatorics/BhatS96' on page 11 undefi -ned on input line 4. - - -LaTeX Warning: Citation `ZanSup04' on page 11 undefined on input line 4. - - -LaTeX Warning: Citation `Bykov2016' on page 11 undefined on input line 14. - - -LaTeX Warning: Citation `ZanSup04' on page 11 undefined on input line 27. - - -LaTeX Warning: Citation `DBLP:journals/combinatorics/BhatS96' on page 11 undefi -ned on input line 27. - - -LaTeX Warning: Citation `Bykov2016' on page 11 undefined on input line 28. - - -LaTeX Warning: Citation `ZanSup04' on page 11 undefined on input line 31. - -[11] - -LaTeX Warning: Citation `Robinson:1981:CS' on page 12 undefined on input line 3 -7. - - -LaTeX Warning: Citation `DBLP:journals/combinatorics/BhatS96' on page 12 undefi -ned on input line 37. - - -LaTeX Warning: Citation `ZanSup04' on page 12 undefined on input line 38. - - -LaTeX Warning: Citation `Robinson:1981:CS' on page 12 undefined on input line 4 -0. - - -LaTeX Warning: Citation `DBLP:journals/combinatorics/BhatS96' on page 12 undefi -ned on input line 43. - - -LaTeX Warning: Citation `ZanSup04' on page 12 undefined on input line 45. - - -LaTeX Warning: Citation `ZanSup04' on page 12 undefined on input line 62. - - -LaTeX Warning: Citation `ZanSup04' on page 12 undefined on input line 84. - -[12] +[9 <./graphe1.pdf> <./graphe2.pdf>]) (./generating.tex [10]) (./hamilton.tex +[11] [12] Overfull \hbox (104.68428pt too wide) in paragraph at lines 119--124 []\T1/cmr/m/it/10 Let now $\OML/cmm/m/it/10 L[] \OT1/cmr/m/n/10 = 0000\OML/cmm/ m/it/10 ; \OT1/cmr/m/n/10 0010\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 0110\OML/cmm/m @@ -1479,170 +1259,13 @@ t/10 ; \OT1/cmr/m/n/10 0100\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 1100\OML/cmm/m/it /10 ;$ [] -Runaway argument? -{2^{\mathsf {N} -n.a_{\mathsf {N}}}{2} \\ c_{\mathsf {N}} = \mathsf {\ETC. -! Paragraph ended before \@genfrac was complete. - - \par -l.189 - -? r -OK, entering \nonstopmode... -! Missing $ inserted. - - $ -l.190 Since $a_ - {\mathsf{N}$ is even, $d_{\mathsf{N}}$ is defined. -I've inserted a begin-math/end-math symbol since I think -you left one out. Proceed, with fingers crossed. - ! Missing } inserted. } l.190 Since $a_{\mathsf{N}$ is even, $d_{\mathsf{N}}$ is defined. -I've inserted something that you may have forgotten. -(See the above.) -With luck, this will get me unwedged. But if you -really didn't forget anything, try typing `2' now; then -my insertion and my current dilemma will both disappear. - - -! LaTeX Error: Something's wrong--perhaps a missing \item. - -See the LaTeX manual or LaTeX Companion for explanation. -Type H for immediate help. - ... - -l.194 \subsection - {Toward a local uniform distribution of switches} -Try typing to proceed. -If that doesn't work, type X to quit. - - -! LaTeX Error: Something's wrong--perhaps a missing \item. - -See the LaTeX manual or LaTeX Companion for explanation. -Type H for immediate help. - ... - -l.194 \subsection - {Toward a local uniform distribution of switches} -Try typing to proceed. -If that doesn't work, type X to quit. - -! Missing } inserted. - - } -l.194 ...a local uniform distribution of switches} - -I've inserted something that you may have forgotten. -(See the above.) -With luck, this will get me unwedged. But if you -really didn't forget anything, try typing `2' now; then -my insertion and my current dilemma will both disappear. - -! Missing \cr inserted. - - \cr -l.194 ...a local uniform distribution of switches} - -I'm guessing that you meant to end an alignment here. - -! Missing $ inserted. - - $ -l.194 ...a local uniform distribution of switches} - -I've inserted a begin-math/end-math symbol since I think -you left one out. Proceed, with fingers crossed. - -) -! Missing $ inserted. - - $ -l.122 - -I've inserted a begin-math/end-math symbol since I think -you left one out. Proceed, with fingers crossed. - -! Missing \endgroup inserted. - - \endgroup -l.122 - -I've inserted something that you may have forgotten. -(See the above.) -With luck, this will get me unwedged. But if you -really didn't forget anything, try typing `2' now; then -my insertion and my current dilemma will both disappear. - -! Missing \right. inserted. - - \right . -l.122 - -I've inserted something that you may have forgotten. -(See the above.) -With luck, this will get me unwedged. But if you -really didn't forget anything, try typing `2' now; then -my insertion and my current dilemma will both disappear. - -! Display math should end with $$. - - \par -l.122 - -The `$' that I just saw supposedly matches a previous `$$'. -So I shall assume that you typed `$$' both times. - - -Overfull \hbox (482.90009pt too wide) detected at line 122 -[] \OMS/cmsy/m/n/10 , [] - [] - -(./stopping.tex [13] - -LaTeX Warning: Citation `LevinPeresWilmer2006' on page 14 undefined on input li -ne 85. - -[14] [15] - -LaTeX Warning: Reference `lm:h' on page 16 undefined on input line 301. - - -LaTeX Warning: Citation `proba' on page 16 undefined on input line 314. - -[16] - -LaTeX Warning: Reference `prop:stop' on page 17 undefined on input line 360. - - -LaTeX Warning: Reference `prop:stop' on page 17 undefined on input line 367. - - -LaTeX Warning: Reference `prop:lambda' on page 17 undefined on input line 368. - - -LaTeX Warning: Reference `lm:stopprime' on page 17 undefined on input line 368. - - -) [17] (./prng.tex - -LaTeX Warning: Reference `CI Algorithm:2' on page 18 undefined on input line 13 -. - - -LaTeX Warning: Reference `sec:hypercube' on page 18 undefined on input line 44. - - - -LaTeX Warning: Reference `eq:Markov:rairo' on page 18 undefined on input line 5 -9. - - -LaTeX Warning: Reference `table:nc' on page 18 undefined on input line 62. - +? +) (./stopping.tex [13] [14] [15] [16] [17]) (./prng.tex [18] LaTeX Warning: Command \textcircled invalid in math mode on input line 64. @@ -1657,11 +1280,6 @@ LaTeX Warning: Command \textcircled invalid in math mode on input line 67. LaTeX Warning: Command \textcircled invalid in math mode on input line 67. -[18] - -LaTeX Warning: Reference `sec:hypercube' on page 19 undefined on input line 76. - - LaTeX Warning: Command \textcircled invalid in math mode on input line 89. @@ -1693,14 +1311,6 @@ LaTeX Warning: Command \textcircled invalid in math mode on input line 172. LaTeX Warning: Command \textcircled invalid in math mode on input line 172. -LaTeX Warning: Reference `The passing rate' on page 19 undefined on input line -214. - - -LaTeX Warning: Reference `The passing rate' on page 19 undefined on input line -217. - - LaTeX Warning: Command \textcircled invalid in math mode on input line 231. @@ -1738,38 +1348,24 @@ Overfull \hbox (4.26556pt too wide) in paragraph at lines 229--250 ) (./conclusion.tex Missing character: There is no p in font dsrom8! Missing character: There is no p in font dsrom8! - [19]) (./main.bbl -Underfull \vbox (badness 10000) has occurred while \output is active [] - - [20] +) [19] (./main.bbl [20] Underfull \hbox (badness 10000) in paragraph at lines 81--84 []\T1/cmr/m/n/8 G. Marsaglia. Diehard: a bat-tery of tests of ran-dom-ness. [] - -Underfull \vbox (badness 10000) has occurred while \output is active [] - - [21]) -[22] (./main.aux) - -LaTeX Warning: There were undefined references. - - -LaTeX Warning: Label(s) may have changed. Rerun to get cross-references right. - - ) +[21]) [22] (./main.aux) ) (\end occurred inside a group at level 1) ### simple group (level 1) entered at line 10 ({) ### bottom level Here is how much of TeX's memory you used: - 22192 strings out of 493105 - 431459 string characters out of 6137072 - 566154 words of memory out of 5000000 - 24950 multiletter control sequences out of 15000+600000 + 20136 strings out of 493304 + 370159 string characters out of 6139871 + 525134 words of memory out of 5000000 + 22909 multiletter control sequences out of 15000+600000 28957 words of font info for 91 fonts, out of 8000000 for 9000 - 1302 hyphenation exceptions out of 8191 - 54i,17n,75p,539b,695s stack positions out of 5000i,500n,10000p,200000b,80000s + 1118 hyphenation exceptions out of 8191 + 48i,17n,75p,539b,695s stack positions out of 5000i,500n,10000p,200000b,80000s {/usr/share/texmf/fonts/enc/dvips/cm-super/cm-super-t1.enc} -Output written on main.pdf (22 pages, 613533 bytes). +Output written on main.pdf (22 pages, 615170 bytes). PDF statistics: 283 PDF objects out of 1000 (max. 8388607) 203 compressed objects within 3 object streams diff --git a/main.pdf b/main.pdf index d5c805b..5124132 100644 Binary files a/main.pdf and b/main.pdf differ diff --git a/stopping.tex b/stopping.tex index 3a07e06..d72f8bb 100644 --- a/stopping.tex +++ b/stopping.tex @@ -144,7 +144,7 @@ A stopping time $\tau$ is a {\emph strong stationary time} if $X_{\tau}$ is independent of $\tau$. -\begin{thrm} +\begin{thrm}\label{thm-sst} If $\tau$ is a strong stationary time, then $d(t)\leq \max_{X\in\Bool^{\mathsf{N}}} \P_X(\tau > t)$. \end{thrm} @@ -362,16 +362,27 @@ One can now prove Theorem~\ref{prop:stop}. \begin{proof} Since $\ts^\prime$ is the time used to obtain $\mathsf{N}-1$ fair bits. Assume that the last unfair bit is $\ell$. One has -$\ts=\ts^\prime+S_{X_\tau,\ell}$, and therefore -$E[\ts] = E[\ts^\prime]+E[S_{X_\tau,\ell}]$. Therefore, -Theorem~\ref{prop:stop} is a direct application of -lemma~\ref{prop:lambda} and~\ref{lm:stopprime}. +$\ts=\ts^\prime+S_{X_\tau,\ell}$, and therefore $E[\ts] = +E[\ts^\prime]+E[S_{X_\tau,\ell}]$. Therefore, Theorem~\ref{prop:stop} is a +direct application of lemma~\ref{prop:lambda} and~\ref{lm:stopprime}. \end{proof} +Now using Markov Inequality, one has $\P_X(\tau > t)\leq \frac{E[\tau]}{t}$. +With $t=32N^2+16N\ln (N+1)$, one obtains: $\P_X(\tau > t)\leq \frac{1}{4}$. +Therefore, using the defintion of $t_{\rm mix)}$ and +Theorem~\ref{thm-sst}, it follows that +$t_{\rm mix}\leq 32N^2+16N\ln (N+1)=O(N^2)$. + + Notice that the calculus of the stationary time upper bound is obtained under the following constraint: for each vertex in the $\mathsf{N}$-cube there are one ongoing arc and one outgoing arc that are removed. The calculus does not consider (balanced) Hamiltonian cycles, which -are more regular and more binding than this constraint. -In this later context, we claim that the upper bound for the stopping time -should be reduced. +are more regular and more binding than this constraint. Moreover, the bound +is obtained using Markov Inequality which is frequently coarse. For the +classical random walkin the $\mathsf{N}$-cube, without removing any +Hamiltonian cylce, the mixing time is in $\Theta(N\ln N)$. +We conjecture that in our context, the mixing time is also in $\Theta(N\ln +N)$. +%In this later context, we claim that the upper bound for the stopping time +%should be reduced.