Topological properties of cellular automata on trees

Gabriele Fici (1) , Francesca Fiorenzi (2)

1 Laboratoire d'Informatique, Signaux, et Systèmes de Sophia-Antipolis (I3S) / Equipe MC3
2 LRI - Laboratoire de Recherche en Informatique

We prove that there do not exist positively expansive cellular automata defined on the full k-ary tree shift (for k>=2). Moreover, we investigate some topological properties of these automata and their relationships, namely permutivity, surjectivity, preinjectivity, right-closingness and openness.

Domaines: Théorie et langage formel [cs.FL]; Complexité [cs.CC]; Mathématique discrète [cs.DM]

Gabriele Fici, Francesca Fiorenzi. Topological properties of cellular automata on trees. AUTOMATA 2012, 2012, France. pp.255-266, ⟨10.4204/EPTCS.90.20⟩. ⟨hal-00946194⟩