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 FatèsConnect in order to contact the contributor Submitted on : Tuesday, April 22, 2014 - 4:17:59 PM Last modification on : Saturday, June 25, 2022 - 7:41:50 PM Long-term archiving on: : Monday, April 10, 2017 - 4:37:56 PM
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⟩