X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/slides_and.git/blobdiff_plain/a462b53d610b423cbe1357e9b35268c0458be0e5..HEAD:/ci.tex?ds=inline

diff --git a/ci.tex b/ci.tex
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@@ -1,32 +1,31 @@
 \vspace{-1.5em}\begin{itemize}
-\item Discrete Iterative System:
+\item SystÃ¨me itÃ©ratif discret:
 \begin{itemize}
-\item $x=(x_1,\dots,x_n)$ : $n$ components, $x_i$ in $\Bool=\{0,1\}$.
-\item A \emph{strategy}  \alert<2>{$(S^{t})^{t \in \Nats}$}: sequence of the
-  components that may be updated at time $t$.
-\item Components evolution: defined for times $t=0,1,2,\ldots$
-by:
+\item $x=(x_1,\dots,x_n)$ : $n$ composants, $x_i \in \Bool=\{0,1\}$.
+\item Une \emph{stratÃ©gie}  \alert<2>{$(J^{t})^{t \in \Nats}$}: suite des 
+  composants qui peuvent Ãªtre mis Ã  jour au temps $t$.
+\item \'Evolution des composants : dÃ©finie pour les temps $t=0,1,2,\ldots$
+par:
 $$  
 \left\{
   \begin{array}{l}   
-    \alert<2>{x^{0}}\in \Bool^{n} \textrm{ and}\\
-    x^{t+1}= (x^{t+1}_1,\dots,x^{t+1}_n) \textrm{ where } 
+    \alert<2>{x^{0}}\in \Bool^{n} \textrm{ et}\\
+    x^{t+1}= (x^{t+1}_1,\dots,x^{t+1}_n) \textrm{ oÃ¹ } 
     x^{t+1}_i =  
     \left\{
       \begin{array}{l}
-        \overline{x^{t}_i} \textrm{ if $i = S^t$}  \\
-        x^t_i \textrm{ otherwise} 
+        \overline{x^{t}_i} \textrm{ si $i = J^t$}  \\
+        x^t_i \textrm{ sinon} 
       \end{array} 
     \right.
   \end{array} 
 \right.
 $$
 \end{itemize}
-\item Theoretical Results~\cite{GuyeuxThese10}\footnote{\bibentry{GuyeuxThese10}}: let $\mathcal{X}$ be 
-$ \llbracket 1 ; n \rrbracket^{\Nats} \times 
-\Bool^n$. We can define a distance $d$ on $\mathcal{X}$ and
-a function $f: \mathcal{X} \rightarrow \mathcal{X}$ from the 
-iterative process
-s.t. $f$ is a continuous and chaotic function.
+\item RÃ©sultats thÃ©oriques: soit 
+$\mathcal{X} = \{1,\ldots, n\}^{\Nats} \times \Bool^n$.
+On peut dÃ©finir une  distance $d$ sur $\mathcal{X}$ et
+une fonction $f: \mathcal{X} \rightarrow \mathcal{X}$ Ã  partir du processus  
+itÃ©ratif t.-q. $f$ est une fonction continue et chaotique.
 \end{itemize}
 
