Ajouts variables LaTeX aux fins de fichiers + corrections quelques typos

diff --git a/chaos.tex b/chaos.tex
index 122c0adce085a17e4da6b6f10a0ab3d1299fc1a6..511a11acab24bdb7d8554928d7afb8cf1c2f5afa 100644 (file)
--- 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}
 
 
 \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}, ...\\
 $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
 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}
 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. 
   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}
 
   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.
 
 
 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 fcf2bad70df52595a399fd2c4c7e30b4d5fc3cb7..a9bf6364160a8485b4009b1fe6eda6ff36f96866 100644 (file)
--- 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.
 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 ace2f7a0fa88d221d44ad301dbaef9ee441cf2d6..3d22441cf0684057f949b1c90f68ed18474f7a97 100644 (file)
--- 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.
 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 17d93803a0d523ddadc31cfe930449bc6a996f41..dc19f08390c9f4a29042af57abbf099de4d86769 100644 (file)
--- 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
 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}
 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 df2a0ee2a27c608426756bebc91d8f809f5b6e47..10463ea2fcf14be284f605bb2cd583b7588d5bc0 100644 (file)
--- a/intro.tex
+++ b/intro.tex
@@ -1,5 +1,5 @@
 The exploitation of chaotic systems to generate pseudorandom sequences
 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
 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.
 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 7384dba978c3b5f9cf00fe3978c29c8f0b7bdd0a..cba5430ad797da97fb199017b0be4f066bf8a3a1 100644 (file)
Binary files a/main.pdf and b/main.pdf differ

diff --git a/main.tex b/main.tex
index 0ea729e508d3c9d78896b0f0d206604dadf19cfe..13d2e2dcbe04df9a317c1bd021559ef80e8f4e34 100644 (file)
--- a/main.tex
+++ b/main.tex
@@ -139,3 +139,9 @@ the classical statistical tests.
 \bibliography{biblio}
 
 \end{document}
 \bibliography{biblio}
 
 \end{document}

+
+%%% Local Variables:
+%%% mode: latex
+%%% ispell-dictionary: "american"
+%%% mode: flyspell
+%%% End:

diff --git a/preliminaries.tex b/preliminaries.tex
index 7c6b050b12a30a50a6b039536b210e8ecb620f66..79611a569f8727decfcb044db490d665926002f5 100644 (file)
--- a/preliminaries.tex
+++ b/preliminaries.tex
@@ -101,3 +101,9 @@ function.
 This is the aims of the next section. 
 
 
 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 5025b4eca7a9d1115ab01749ab0afe33f06660bf..6af2803ad6918b63ebfd02793a74d5e87399ab41 100644 (file)
--- 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 
 
 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.
 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}
 
 
 \end{table}
 
 

+%%% Local Variables:
+%%% mode: latex
+%%% TeX-master: "main"
+%%% ispell-dictionary: "american"
+%%% mode: flyspell
+%%% End:

diff --git a/stopping.tex b/stopping.tex
index 409dd83c971a5402faba645fedce5ebf85c777ae..fb0b9e0dec27c2dc2215ea2e80b7304e0a034f91 100644 (file)
--- 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 
 
 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
 (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.  
 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}
 $$
 \caption{Average Stopping Time}\label{table:stopping:moy}
 \end{table}

+
+%%% Local Variables:
+%%% mode: latex
+%%% TeX-master: "main"
+%%% ispell-dictionary: "american"
+%%% mode: flyspell
+%%% End: