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Communication dans un congrès
On Local Symmetries and Universality in Cellular Automata
Abstract : Cellular automata (CA) are dynamical systems defined by a finite local rule but they are studied for their global dynamics. They can exhibit a wide range of complex behaviours and a celebrated result is the existence of (intrinsically) universal CA, that is CA able to fully simulate any other CA. In this paper, we show that the asymptotic density of universal cellular automata is 1 in several families of CA defined by local symmetries. We extend results previously established for captive cellular automata in two significant ways. First, our results apply to well-known families of CA (e.g. the family of outer-totalistic CA containing the Game of Life) and, second, we obtain such density results with both increasing number of states and increasing neighbourhood. Moreover, thanks to universality-preserving encodings, we show that the universality problem remains undecidable in some of those families.
https://hal.inria.fr/inria-00359174
Contributeur : Publications Loria <>
Soumis le : vendredi 6 février 2009 - 10:58:12
Dernière modification le : lundi 9 juillet 2018 - 17:04:02
Document(s) archivé(s) le : mardi 8 juin 2010 - 21:57:25
Contributeur : Publications Loria <>
Soumis le : vendredi 6 février 2009 - 10:58:12
Dernière modification le : lundi 9 juillet 2018 - 17:04:02
Document(s) archivé(s) le : mardi 8 juin 2010 - 21:57:25
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