X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/rairo15.git/blobdiff_plain/5207d2fe1ec5d598398e217569e592f0fb6a07ff..b2ddddea6b545cf4a7e8d21e3ba00b224a0e6c3b:/prng.tex

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}