Surjective multidimensional cellular automata are non-wandering: A combinatorial proof

Luigi Acerbi (1) , Alberto Dennunzio (1) , Enrico Formenti (2, 3)

1 DISCo - Dipartimento di Informatica Sistemistica e Comunicazione
2 I3S - Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis
3 Laboratoire I3S - MDSC - Modèles Discrets pour les Systèmes Complexes

A combinatorial proof that surjective D-dimensional CA are non-wandering is given. This answers an old open question stated in Blanchard and Tisseur (2000) [3]. Moreover, an explicit upper bound for the return time is given.

Mots clés: Combinatorial problems; Multidimensional cellular automata; Symbolic dynamics; Discrete dynamical systems

Domaines: Informatique [cs]; Complexité [cs.CC]; Mathématique discrète [cs.DM]; Systèmes dynamiques [math.DS]; Automates cellulaires et gaz sur réseau [nlin.CG]; Dynamique Chaotique [nlin.CD]; Adaptation et Systèmes auto-organisés [nlin.AO]

Luigi Acerbi, Alberto Dennunzio, Enrico Formenti. Surjective multidimensional cellular automata are non-wandering: A combinatorial proof. Information Processing Letters, 2013, 113 (5-6), pp.156-159. ⟨10.1016/j.ipl.2012.12.009⟩. ⟨hal-01312575⟩