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A note on the fast convergence of asynchronous Elementary Cellular Automata

Nazim Fatès

Abstract

We tackle the problem of the classification of elementary cellular automata when the cells are updated in with a fully asynchronous scheme (one cell is selected at random at each time step). We establish a proof of convergence in logarithmic time as a function of the size of the automaton. Techniques involve a direct Markov chain analysis or the construction of potential function whose convergence rate is bounded by a particular martingale.
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hal-00981691 , version 1 (22-04-2014)

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Nazim Fatès. A note on the fast convergence of asynchronous Elementary Cellular Automata. 19th International Workshop, AUTOMATA 2013,, Sep 2013, Gießen, Germany. pp.31-45, ⟨10.1007/978-3-642-40867-0_3⟩. ⟨hal-00981691⟩
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