From: Sylvain C-V <contasss@loria.fr>
Date: Thu, 23 Jun 2016 15:24:35 +0000 (+0200)
Subject: Ajouts variables LaTeX aux fins de fichiers + corrections quelques typos
X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/16dcc.git/commitdiff_plain/236f25b2f3a081b11c71bedad6d044d695ce2cca?ds=sidebyside
Ajouts variables LaTeX aux fins de fichiers + corrections quelques typos
---
diff --git a/chaos.tex b/chaos.tex
index 122c0ad..511a11a 100644
--- a/chaos.tex
+++ b/chaos.tex
@@ -247,7 +247,7 @@ $\check{u}^{v^0}$ (on $n$ digits), ..., $\check{u}^{\check{v}^0-1}$ (on $n$ digi
\begin{xpl}
-Consider for instance that $\mathsf{N}=13$, $\mathcal{P}=\{1,2,11\}$ (so $\mathsf{p}=3$), and that
+Consider for instance that $\mathsf{N}=13$, $\mathcal{P}=\{1,2,11\}$ (so $\mathsf{p}=2$), and that
$s=\left\{
\begin{array}{l}
u=\underline{6,} ~ \underline{11,5}, ...\\
@@ -425,7 +425,7 @@ $\mathcal{P}=\{2,3\}$. The graphs of iterations are given in
The \textsc{Figure~\ref{graphe1}} shows what happens when
displaying each iteration result.
On the contrary, the \textsc{Figure~\ref{graphe2}} explicits the behaviors
-when always applying 2 or 3 modification and next outputing results.
+when always applying either 2 or 3 modifications before generating results.
Notice that here, orientations of arcs are not necessary
since the function $f_0$ is equal to its inverse $f_0^{-1}$.
\end{xpl}
@@ -521,7 +521,7 @@ and only if its iteration graph $\Gamma_{\mathcal{P}}(f)$ is strongly connected.
In this context, $\mathcal{P}$ is the singleton $\{b\}$.
If $b$ is even, any vertex $e$ of $\Gamma_{\{b\}}(f_0)$ cannot reach
its neighborhood and thus $\Gamma_{\{b\}}(f_0)$ is not strongly connected.
- If $b$ is even, any vertex $e$ of $\Gamma_{\{b\}}(f_0)$ cannot reach itself
+ If $b$ is odd, any vertex $e$ of $\Gamma_{\{b\}}(f_0)$ cannot reach itself
and thus $\Gamma_{\{b\}}(f_0)$ is not strongly connected.
\end{proof}
@@ -530,4 +530,9 @@ functions and a iteration number $b$
such that $\Gamma_{\{b\}}$ is strongly connected.
-
\ No newline at end of file
+%%% Local Variables:
+%%% mode: latex
+%%% TeX-master: "main"
+%%% ispell-dictionary: "american"
+%%% mode: flyspell
+%%% End:
diff --git a/conclusion.tex b/conclusion.tex
index fcf2bad..a9bf636 100644
--- a/conclusion.tex
+++ b/conclusion.tex
@@ -33,3 +33,10 @@ Conditions allowing the reduction of the stopping-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 iterations.
+
+%%% Local Variables:
+%%% mode: latex
+%%% TeX-master: "main"
+%%% ispell-dictionary: "american"
+%%% mode: flyspell
+%%% End:
diff --git a/generating.tex b/generating.tex
index ace2f7a..3d22441 100644
--- a/generating.tex
+++ b/generating.tex
@@ -76,3 +76,10 @@ from the
The next section presents how to build balanced Hamiltonian cycles in the
$\mathsf{N}$-cube with the objective to embed them into the
pseudorandom number generator.
+
+%%% Local Variables:
+%%% mode: latex
+%%% TeX-master: "main"
+%%% ispell-dictionary: "american"
+%%% mode: flyspell
+%%% End:
diff --git a/hamilton.tex b/hamilton.tex
index 17d9380..dc19f08 100644
--- a/hamilton.tex
+++ b/hamilton.tex
@@ -23,7 +23,7 @@ $\mathsf{N}$ cube.
Obviously, the number of iterations $b$ has to be sufficiently large
to provide a uniform output distribution.
To reduce the number of iterations, the provided Gray code
-should ideally possess the both balanced and locally balanced properties.
+should ideally possess both balanced and locally balanced properties.
However, none of the two algorithms is compatible with the second one:
balanced Gray codes that are generated by state of the art works~\cite{ZanSup04,DBLP:journals/combinatorics/BhatS96} are not locally balanced. Conversely,
locally balanced Gray codes yielded by Igor Bykov approach~\cite{Bykov2016}
@@ -328,3 +328,9 @@ Notice that all such choices lead to a hamiltonian path.
+%%% Local Variables:
+%%% mode: latex
+%%% TeX-master: "main"
+%%% ispell-dictionary: "american"
+%%% mode: flyspell
+%%% End:
diff --git a/intro.tex b/intro.tex
index df2a0ee..10463ea 100644
--- a/intro.tex
+++ b/intro.tex
@@ -1,5 +1,5 @@
The exploitation of chaotic systems to generate pseudorandom sequences
-is an hot topic~\cite{915396,915385,5376454}. Such systems are
+is a hot topic~\cite{915396,915385,5376454}. Such systems are
fundamentally chosen due to their unpredictable character and their
sensitiveness to initial conditions. In most cases, these generators
simply consist in iterating a chaotic function like the logistic
@@ -111,3 +111,10 @@ Section~\ref{sec:prng} gives practical results on evaluating the PRNG
against the NIST suite. This research work ends by a conclusion
section, where the contribution is summarized and intended future work
is outlined.
+
+%%% Local Variables:
+%%% mode: latex
+%%% TeX-master: "main"
+%%% ispell-dictionary: "american"
+%%% mode: flyspell
+%%% End:
diff --git a/main.pdf b/main.pdf
index 7384dba..cba5430 100644
Binary files a/main.pdf and b/main.pdf differ
diff --git a/main.tex b/main.tex
index 0ea729e..13d2e2d 100644
--- a/main.tex
+++ b/main.tex
@@ -139,3 +139,9 @@ the classical statistical tests.
\bibliography{biblio}
\end{document}
+
+%%% Local Variables:
+%%% mode: latex
+%%% ispell-dictionary: "american"
+%%% mode: flyspell
+%%% End:
diff --git a/preliminaries.tex b/preliminaries.tex
index 7c6b050..79611a5 100644
--- a/preliminaries.tex
+++ b/preliminaries.tex
@@ -101,3 +101,9 @@ function.
This is the aims of the next section.
+%%% Local Variables:
+%%% mode: latex
+%%% TeX-master: "main"
+%%% ispell-dictionary: "american"
+%%% mode: flyspell
+%%% End:
diff --git a/prng.tex b/prng.tex
index 5025b4e..6af2803 100644
--- a/prng.tex
+++ b/prng.tex
@@ -54,7 +54,8 @@ it preserves this property.
For each number $\mathsf{N}=4,5,6,7,8$ of bits, we have generated
the functions according to the method
-given in Sect.~\ref{sec:SCCfunc}.
+given in Sect.~\ref{sec:SCCfunc}.
+% MENTION FILTRAGE POSSIBLE LORS DE CONSTRUCTION... (SCV)
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.
@@ -253,3 +254,9 @@ Linear Complexity& 0.719 (1.0)& 0.739 (0.99)& 0.759 (0.98)& 0.122 (0.97)& 0.514
\end{table}
+%%% Local Variables:
+%%% mode: latex
+%%% TeX-master: "main"
+%%% ispell-dictionary: "american"
+%%% mode: flyspell
+%%% End:
diff --git a/stopping.tex b/stopping.tex
index 409dd83..fb0b9e0 100644
--- a/stopping.tex
+++ b/stopping.tex
@@ -40,11 +40,11 @@ P=\dfrac{1}{6} \left(
A specific random walk in this modified hypercube is first
introduced (See section~\ref{sub:stop:formal}). We further
-theoretical study this random walk to
-provide a upper bound of fair sequences
+ study this random walk in a theoretical way to
+provide an upper bound of fair sequences
(See section~\ref{sub:stop:bound}).
We finally complete these study with experimental
-results that reduce this bound (Sec.~\ref{sub:stop:stop}).
+results that reduce this bound (Sec.~\ref{sub:stop:exp}).
Notice that for a general references on Markov chains
see~\cite{LevinPeresWilmer2006},
and particularly Chapter~5 on stopping times.
@@ -422,3 +422,10 @@ $$
$$
\caption{Average Stopping Time}\label{table:stopping:moy}
\end{table}
+
+%%% Local Variables:
+%%% mode: latex
+%%% TeX-master: "main"
+%%% ispell-dictionary: "american"
+%%% mode: flyspell
+%%% End: