From: Christophe Guyeux Date: Fri, 13 Mar 2015 17:12:24 +0000 (+0100) Subject: relecture conclusion X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/rairo15.git/commitdiff_plain/e61474ab27a007c2d18a49336c3f7f91d889a444 relecture conclusion --- diff --git a/conclusion.tex b/conclusion.tex index 35b815c..0b51092 100644 --- a/conclusion.tex +++ b/conclusion.tex @@ -13,19 +13,20 @@ % pertinence de l'approche théorique. % -In this article, we have proven that the most general chaotic iterations based PRNG -satisfy the property of chaos as defined by Devaney. We then have shown how to generate -such functions together with the number of iterations, leading to strongly connected +In this article, we have proven that the most general chaotic iterations based PRNG, which embeds +an iteration function, satisfies in some cases the property of chaos +as defined by Devaney. We then have shown how to generate such functions together +with the related number of iterations, leading to strongly connected iteration graphs and thus to chaos for the associated pseudorandom number generators. By removing some paths in the hypercube, we then have provided examples of such graphs -that lead to chaos, while relating these graphs to the PRNG problem under consideration. +that lead to chaos, while linking these graphs to the PRNG problem under consideration. In future work, we intend to understand the link between succeeded or failed statistical tests and the properties of chaos for the associated asynchronous iterations. By doing so, relations between desired statistically unbiased behaviors and topological properties will be understood, leading to better choices in iteration functions. Conditions allowing the reduction of the mixing time will be investigated too, while other modifications of the hypercube -will be regarded, in order to enlarge the set of known chaotic and random asynchronous +will be regarded in order to enlarge the set of known chaotic and random asynchronous iterations. %