# Subshift attractors of cellular automata

1 Laboratoire d'Informatique, Signaux, et Systèmes de Sophia-Antipolis (I3S) / Equipe MC3
Laboratoire I3S - MDSC - Modèles Discrets pour les Systèmes Complexes
Abstract : 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 $p\in Z$.
Document type :
Journal articles
Domain :
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-00311968
Contributor : Enrico Formenti <>
Submitted on : Friday, August 22, 2008 - 6:06:26 PM
Last modification on : Monday, November 5, 2018 - 3:48:02 PM

### Identifiers

• HAL Id : hal-00311968, version 1

### Citation

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

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