X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/rairo15.git/blobdiff_plain/428720e875baf64678c06f2c75ae55185b18d81a..70b2c7214ae3421e58d225cbbb21fafbebcd8acc:/intro.tex

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@@ -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