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.
https://hal.inria.fr/hal-00981691
Contributor : Nazim Fatès
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Submitted on : Tuesday, April 22, 2014 - 4:17:59 PM
Last modification on : Tuesday, December 18, 2018 - 4:40:21 PM
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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⟩
