From: Christophe Guyeux <christophe.guyeux@univ-fcomte.fr>
Date: Fri, 13 Mar 2015 16:40:20 +0000 (+0100)
Subject: plan de l'intro
X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/rairo15.git/commitdiff_plain/a4822f9546c111a918ccfc748828076bcfe1202a?ds=sidebyside

plan de l'intro
---

diff --git a/intro.tex b/intro.tex
index f4ed222..dafa1cf 100644
--- a/intro.tex
+++ b/intro.tex
@@ -215,6 +215,16 @@ theoretical properties but with a reduced mixing time.
 % sur une batterie de tests.
 
 
+The remainder of this article is organized as follows. The next section is devoted to 
+preliminaries, basic notations, and terminologies regarding asynchronous iterations.
+Then, in Section~\ref{sec:proofOfChaos}, Devaney's definition of chaos is recalled
+while the proofs of chaos of our most general PRNGs is provided. Section~\ref{sec:SCCfunc} shows how to generate functions and a number of iterations such that the iteration graph is strongly connected, making the
+PRNG chaotic. The next section focus on examples of such graphs obtained by modifying the 
+hypercube, while Section~\ref{sec:prng} establishes the link between the theoretical study and
+pseudorandom number generation. 
+This research work ends by a conclusion section, where the contribution is summarized and
+intended future work is outlined.
+
 % Le reste de ce document est organisé comme suit. 
 % La section~\ref{section:chaos} présente ce qu'est un système dynamique discret booléen itérant une fonction $f$.
 % La chaoticité de la fonction engendrée $G_f$ est caractérisée en 
diff --git a/main.tex b/main.tex
index 2c42373..4f8d3a3 100644
--- a/main.tex
+++ b/main.tex
@@ -115,13 +115,13 @@ 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{Random walk on the modified Hypercube}\label{sec:hypercube}
 \input{stopping}
 
 % Donner la borne du stopping time quand on marche dedans (nouveau). 
@@ -135,7 +135,7 @@ the classical statsitcal tests.
 %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}
 \JFC{ajouter ici les expérimentations}