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?hp=e1fe6e435ee452003a7135763d26e2320756398c

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: