From: Christophe Guyeux Date: Sun, 15 Mar 2015 08:22:49 +0000 (+0100) Subject: Fin de la relecture des exp X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/rairo15.git/commitdiff_plain/b2ddddea6b545cf4a7e8d21e3ba00b224a0e6c3b?ds=sidebyside;hp=5207d2fe1ec5d598398e217569e592f0fb6a07ff Fin de la relecture des exp --- diff --git a/prng.tex b/prng.tex index c565970..3776d09 100644 --- a/prng.tex +++ b/prng.tex @@ -53,8 +53,8 @@ it preserves this property. For each number $\mathsf{N}=4,5,6,7,8$ of bits, we have generated -the functions according the method -given in Sect.~\ref{sec:SCCfunc} . +the functions according to the method +given in Sect.~\ref{sec:SCCfunc}. For each $\mathsf{N}$, we have then restricted this evaluation to the function whose Markov Matrix (issued from Eq.~(\ref{eq:Markov:rairo})) has the smallest practical mixing time. @@ -69,9 +69,9 @@ it is obtained as the binary value of the fourth element in the second list (namely~14). In this table the column -which is labeled with $b$ (respectively by $E[\tau]$) +that is labeled with $b$ (respectively by $E[\tau]$) gives the practical mixing time -where the deviation to the standard distribution is less than $10^{-6}$ +where the deviation to the standard distribution is lesser than $10^{-6}$ (resp. the theoretical upper bound of stopping time as described in Sect.~\ref{sec:hypercube}). @@ -214,7 +214,9 @@ If the value $\mathbb{P}_T$ of any test is smaller than 0.0001, the sequences ar and the generator is unsuitable. Table~\ref{The passing rate} shows $\mathbb{P}_T$ of sequences based on discrete chaotic iterations using different schemes. If there are at least two statistical values in a test, this test is marked with an asterisk and the average value is computed to characterize the statistics. -We can see in Table \ref{The passing rate} that all the rates are greater than 97/100, \textit{i. e.}, all the generators pass the NIST test. +We can see in Table \ref{The passing rate} that all the rates are greater than 97/100, \textit{i.e.}, all the generators +achieve to pass the NIST battery of tests. + \begin{table}