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Article Dans Une Revue Nonlinearity Année : 2007

Subshift attractors of cellular automata

Résumé

A subshift attractor is a two-sided subshift which is an attractor of a cellular automaton. We prove that each subshift attractor is chain-mixing, contains a configuration which is both F-periodic and $\sigma$-periodic and the complement of its language is recursively enumerable. We prove that a subshift of finite type is an attractor of a cellular automaton iff it is mixing. We identify a class of chain-mixing sofic subshifts which are not subshift attractors. We construct a cellular automaton whose maximal attractor is a non-sofic mixing subshift, answering a question raised in Maass. We show that a cellular automaton is surjective on its small quasi-attractor which is the non-empty intersection of all subshift attractors of all $F^q\sigma^p$, where $q>0$ and $p\in Z$.
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Dates et versions

hal-00311968 , version 1 (22-08-2008)

Identifiants

  • HAL Id : hal-00311968 , version 1

Citer

Enrico Formenti, Petr Kurka. Subshift attractors of cellular automata. Nonlinearity, 2007, 20, pp.105-117. ⟨hal-00311968⟩
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