A note on the fast convergence of asynchronous Elementary Cellular Automata

Nazim Fatès 1
1 MAIA - Autonomous intelligent machine
Inria Nancy - Grand Est, LORIA - AIS - Department of Complex Systems, Artificial Intelligence & Robotics
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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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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