Bruno Martin's Publications
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Ph.D. thesis: Cellular
Automata, Information and Chaos (french).
- 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):