Bruno Martin's Publications

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Ph.D. thesis: Cellular Automata, Information and Chaos (french).
  • Abstract:
    Starting from the available classifications of cellular automata, we improve the best one. Thanks to a measure on the set of configurations and to a shift-invariant pseudo-distance, we introduce the notion of $\mu$-sensitivity to initial conditions. This notion allows us to show that some rules are chaotic or non chaotic depending on the initial configuration. We also introduce the apparent entropy notion which explains why the evolution of cellular automata looks complex. Finally, we prove new results on algebraic classifications by pointing out a conservation law for the particles in Wolfram's rule $54$.

    Revenue Management (stochastic optimization):
    Cellular Automata: Linear Logic: