main.tex

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  33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  34 % Définitions personnelles
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  84
  85
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  87
  88
  89 \title{Random Walk in a N-cube Without Hamiltonian Cycle
  90   to Chaotic Pseudorandom Number Generation: Theoretical and Practical
  91   Considerations}
  92
  93 \begin{document}
  94
  95 \author{Jean-François Couchot, Christophe Guyeux, Pierre-Cyrille Heam}
  96 \address{Institut FEMTO-ST, Université de Franche-Comté, Belfort, France}
  97
  98
  99
 100 \begin{abstract}
 101 This paper is dedicated to the design of chaotic random generators
 102 and extends previous works proposed by some of the authors.
 103 We propose a theoretical framework proving both the chaotic properties and
 104 that the limit distribution is uniform.
 105 A theoretical bound on the stationary time is given and
 106 practical experiments show that the generators successfully pass
 107 the classical statistical tests.
 108 \end{abstract}
 109
 110 \maketitle
 111
 112 \section{Introduction}
 113 \input{intro}
 114
 115  \section{\uppercase{Preliminaries}}\label{sec:preliminaries}
 116 \input{preliminaries}
 117
 118 \section{Proof Of Chaos}\label{sec:proofOfChaos}
 119 \input{chaos}
 120
 121 \section{Functions with Strongly Connected $\Gamma_{\{b\}}(f)$}\label{sec:SCCfunc}
 122 \input{generating}
 123
 124 \section{Stopping Time}\label{sec:hypercube}
 125 \input{stopping}
 126
 127 \section{Experiments}\label{sec:prng}
 128 \input{prng}
 129
 130
 131
 132 \section{Conclusion}
 133 \input{conclusion}
 134
 135 %\acknowledgements{...}
 136
 137 \bibliographystyle{alpha}
 138 \bibliography{biblio}
 139
 140 \end{document}