Cellular automata between sofic tree shifts

  • Authors:

  • Tullio Ceccherini-Silberstein;Michel Coornaert;Francesca Fiorenzi;Zoran Šunić

  • Affiliations:

  • Dipartimento di Ingegneria, Universití del Sannio, C.so Garibaldi 107, 82100 Benevento, Italy;Institut de Recherche Mathématique Avancée, UMR 7501, Université de Strasbourg et CNRS, 7 rue René-Descartes, 67000 Strasbourg, France;Laboratoire de Recherche en Informatique, Université Paris-Sud 11, 91405 Orsay Cedex, France;Department of Mathematics, Texas A&M University, MS-3368, College Station, TX 77843-3368, USA

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2013

Quantified Score

Hi-index 5.23

Visualization

Abstract

We study the sofic tree shifts of A^@S^^^@?, where @S^@? is a regular rooted tree of finite rank. In particular, we give their characterization in terms of unrestricted Rabin automata. We show that if X@?A^@S^^^@? is a sofic tree shift, then the configurations in X whose orbit under the shift action is finite are dense in X, and, as a consequence of this, we deduce that every injective cellular automata @t:X-X is surjective. Moreover, a characterization of sofic tree shifts in terms of general Rabin automata is given. We present an algorithm for establishing whether two unrestricted Rabin automata accept the same sofic tree shift or not. This allows us to prove the decidability of the surjectivity problem for cellular automata between sofic tree shifts. We also prove the decidability of the injectivity problem for cellular automata defined on a tree shift of finite type.