stoping

[rairo15.git] / main.tex

diff --git a/main.tex b/main.tex
index 5fa40f49c90e3753b0ccb7a792e66d38ea9cb201..9e544ca0cc3b052ba3638631921f6d4c411ec1a9 100644 (file)
--- a/main.tex
+++ b/main.tex
@@ -1,15 +1,18 @@
 \documentclass{ita}
 \usepackage{graphicx}
 \documentclass{ita}
 \usepackage{graphicx}

+\usepackage{caption}
+\usepackage{subcaption}
+

 \usepackage{dsfont}
 \usepackage{stmaryrd}
 \usepackage{dsfont}
 \usepackage{stmaryrd}

-\usepackage[font=footnotesize]{subfig}
+%\usepackage[font=footnotesize]{subfig}

 \usepackage{ifthen}
 \usepackage{color}
 \usepackage{algorithm2e}
 \usepackage{epstopdf}
 \usepackage{ifthen}
 \usepackage{color}
 \usepackage{algorithm2e}
 \usepackage{epstopdf}

+%\usepackage{ntheorem}

 
 

-
-\usepackage[latin1]{inputenc}
+\usepackage[utf8]{inputenc}

 \usepackage[T1]{fontenc} 
 \usepackage[english]{babel}
 \usepackage{amsmath,amssymb,latexsym,eufrak,euscript}
 \usepackage[T1]{fontenc} 
 \usepackage[english]{babel}
 \usepackage{amsmath,amssymb,latexsym,eufrak,euscript}


@@ -28,7 +31,7 @@
 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

-% Définitions personnelles
+% Définitions personnelles

 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 \definecolor{bleuclair}{rgb}{0.75,0.75,1.0}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 \definecolor{bleuclair}{rgb}{0.75,0.75,1.0}


@@ -55,23 +58,13 @@
 \def \ts {\tau_{\rm stop}}
 
 
 \def \ts {\tau_{\rm stop}}
 
 

-% \theoremstyle{plain}
-% \theoremheaderfont{\normalfont\bfseries\sc}
-% \theorembodyfont{\slshape}
-% \theoremsymbol{\ensuremath{\diamondsuit}}
-% \theoremprework{\bigskip}
-% \theoremseparator{.}
-\newtheorem{Def}{\underline{Definition}}
-\newtheorem{Lemma}{\underline{Lemma}}
-\newtheorem{Theo}{\underline{Theorem}}
-% \theoremheaderfont{\sc}
-% \theorembodyfont{\upshape}
-% \theoremstyle{nonumberplain}
-% \theoremseparator{}
-% \theoremsymbol{\rule{1ex}{1ex}}
-\newtheorem{Proof}{Proof}
+\newtheorem{Def}{Definition}
+%\newtheorem{Lemma}{\underline{Lemma}}
+\newtheorem{Theo}{Theorem}
+\newtheorem{Corollary}{Corollary}
+\newtheorem{Lemma}{Lemma}

 \newtheorem{proposition}{Proposition}
 \newtheorem{proposition}{Proposition}

-\newtheorem{xpl}{Running Example}
+\newtheorem*{xpl}{Running Example}

 
 \newcommand{\vectornorm}[1]{\ensuremath{\left|\left|#1\right|\right|_2}}
 %\newcommand{\ie}{\textit{i.e.}}
 
 \newcommand{\vectornorm}[1]{\ensuremath{\left|\left|#1\right|\right|_2}}
 %\newcommand{\ie}{\textit{i.e.}}


@@ -93,65 +86,62 @@
 
 
 
 
 
 

-\title{XXX}
+\title{Random Walk in a N-cube Without Hamiltonian Cycle 
+  to Chaotic Pseudorandom Number Generation: Theoretical and Practical 
+  Considerations}

 
 \begin{document}
 
 
 \begin{document}
 

-\author{Jean-François Couchot, Christophe Guyeux, Pierre-Cyrile Heam}
-\address{Institut FEMTO-ST, Université de Franche-Comté, Belfort, France}
+\author{Jean-François Couchot, Christophe Guyeux, Pierre-Cyrile Heam}
+\address{Institut FEMTO-ST, Université de Franche-Comté, Belfort, France}

 
 

-%\author{Sylvain Contassot-Vivier}
-%\address{Loria - UMR 7503, Université de Lorraine, Nancy, France}

 
 

-\date{...}

 
 \begin{abstract}
 
 \begin{abstract}

-This   paper  extends   the  results   presented  in~\cite{bcgr11ip}
-and~\cite{chgw14oip} by using the \emph{chaotic} updating mode, in the sense
-of F.  Robert~\cite{Robert}.  In this mode, several components of the system
-may be  updated at each iteration.   At the theoretical level,  we show that
-    the properties of  chaos and uniformity of the  obtained PRNG are preserved.
-    At  the practical level,  we show  that the  algorithm that  builds strongly
-    connected  iteration graphs,  with doubly  stochastic Markov  matrix,  has a
-    reduced mixing time.
+This paper is dedicated to the design of chaotic random generators
+and extends previous works proposed by some of the authors.
+We propose a theoretical framework proving both the chaotic properties and
+that the limit distribution is uniform.
+A theoretical bound on the stationary time is given and
+practical experiments show that the generators successfully passe
+the classical statsitcal tests.

 \end{abstract}
 
 \end{abstract}
 

+\maketitle
+

 \section{Introduction}
 \section{Introduction}

-%\input{intro}
+\input{intro}

 
  \section{\uppercase{Preliminaries}}\label{sec:preliminaries}
 \input{preliminaries}
 
 
  \section{\uppercase{Preliminaries}}\label{sec:preliminaries}
 \input{preliminaries}
 

-\section{Proof Of Chaos}
-\JFC{Enlever les refs aux PRNGs, harmoniser l'exemple}
+\section{Proof Of Chaos}\label{sec:proofOfChaos}

 \input{chaos}
 
 \input{chaos}
 

-\section{Generating....}
-\JFC{Reprendre Mons en synthétisant... conclusion: n-cube moins hamitonien.
-question efficacité d'un tel algo}
-%\input{chaos}
+\section{Functions with Strongly Connected $\Gamma_{\{b\}}(f)$}\label{sec:SCCfunc}
+\input{generating}

 
 

-\section{Random walk on the modified Hypercube}
+\section{Random walk on the modified Hypercube}\label{sec:hypercube}

 \input{stopping}
 
 % Donner la borne du stopping time quand on marche dedans (nouveau). 
 \input{stopping}
 
 % Donner la borne du stopping time quand on marche dedans (nouveau). 

-% Énoncer le problème de la taille de cette borne
+% Énoncer le problème de la taille de cette borne

 % (elle est certes finie, mais grande). 
 
 
 
 
 %\section{Quality study of the strategy}
 % (elle est certes finie, mais grande). 
 
 
 
 
 %\section{Quality study of the strategy}

-%6) Se pose alors la question de comment générer une stratégie de "bonne qualité". Par exemple, combien de générateurs aléatoires embarquer ? (nouveau)
+%6) Se pose alors la question de comment générer une stratégie de "bonne qualité". Par exemple, combien de générateurs aléatoires embarquer ? (nouveau)

 
 
 
 

-\section{Application to Pseudorandom Number Generation}
+\section{Application to Pseudorandom Number Generation}\label{sec:prng}

 \input{prng}
 \input{prng}

-\JFC{ajouter ici les expérimentations}
+\JFC{ajouter ici les expérimentations}

 
 
 \section{Conclusion}
 
 
 \section{Conclusion}

-%\input{conclusion}
+\input{conclusion}

 
 %\acknowledgements{...}
 
 
 %\acknowledgements{...}