X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/rairo15.git/blobdiff_plain/7adee4533e3b5462c283ce03d98ef5c440600e42..ce7a3e374f8ea8cd61b0cfebb7a7eae7852f75e1:/main.tex?ds=inline

diff --git a/main.tex b/main.tex
index 2c42373..465fbf5 100644
--- a/main.tex
+++ b/main.tex
@@ -58,12 +58,6 @@
 \def \ts {\tau_{\rm stop}}
 
 
-\newtheorem{Def}{Definition}
-%\newtheorem{Lemma}{\underline{Lemma}}
-\newtheorem{Theo}{Theorem}
-\newtheorem{Corollary}{Corollary}
-\newtheorem{Lemma}{Lemma}
-\newtheorem{proposition}{Proposition}
 \newtheorem*{xpl}{Running Example}
 
 \newcommand{\vectornorm}[1]{\ensuremath{\left|\left|#1\right|\right|_2}}
@@ -92,10 +86,12 @@
 
 \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-Cyrille Heam}
+\address{FEMTO-ST Institute, University of Franche-Comté, Belfort, France}
 
+\keywords{Pseudorandom Number Generator, Theory of Chaos, Markov Matrice, Hamiltonian Path, Mixing Time, Stopping Time, Statistical Test}
 
+\subjclass{34C28, 37A25,11K45}
 
 \begin{abstract}
 This paper is dedicated to the design of chaotic random generators
@@ -103,8 +99,8 @@ 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.
+practical experiments show that the generators successfully pass
+the classical statistical tests.
 \end{abstract}
 
 \maketitle
@@ -115,33 +111,22 @@ the classical statsitcal tests.
  \section{\uppercase{Preliminaries}}\label{sec:preliminaries}
 \input{preliminaries}
 
-\section{Proof Of Chaos}
+\section{Proof Of Chaos}\label{sec:proofOfChaos}
 \input{chaos}
 
-\section{Functions with Strongly Connected $\Gamma_{\{b\}}(f)$}
+\section{Functions with Strongly Connected $\Gamma_{\{b\}}(f)$}\label{sec:SCCfunc}
 \input{generating}
 
-\section{Random walk on the modified Hypercube}
+\section{Stopping Time}\label{sec:hypercube}
 \input{stopping}
 
-% Donner la borne du stopping time quand on marche dedans (nouveau). 
-% Énoncer le problème de la taille de cette borne
-% (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)
-
-
-\section{Application to Pseudorandom Number Generation}
+\section{Experiments}\label{sec:prng}
 \input{prng}
-\JFC{ajouter ici les expérimentations}
+
 
 
 \section{Conclusion}
-%\input{conclusion}
+\input{conclusion}
 
 %\acknowledgements{...}