This battery can be found in the well-known TestU01 package~\cite{LEcuyerS07}.
Chaos, for its part, refers to the well-established definition of a
chaotic dynamical system proposed by Devaney~\cite{Devaney}.
-
+\begin{color}{red}
+More precisely, each time we performed a test on a PRNG, we ran it
+twice in order to observe if all p-values are inside [0.01, 0.99]. In
+fact, we observed that few p-values (less than ten) are sometimes
+outside this interval but inside [0.001, 0.999], so that is why a
+second run allows us to confirm that the values outside are not for
+the same test. With this approach all our PRNGs pass the {\it
+ BigCrush} successfully and all p-values are at least once inside
+[0.01, 0.99].
+\end{color}
In a previous work~\cite{bgw09:ip,guyeux10} we have proposed a post-treatment on PRNGs making them behave
as a chaotic dynamical system. Such a post-treatment leads to a new category of
two PRNGs as inputs. These two generators are mixed with chaotic iterations,
leading thus to a new PRNG that
\begin{color}{red}
-should improves the statistical properties of each
+should improve the statistical properties of each
generator taken alone.
Furthermore, the generator obtained by this way possesses various chaos properties that none of the generators used as input
present.
