The Dynamics of Cellular Automata in Shift-Invariant Topologies

Abstract. We study the dynamics of cellular automata, and more specifically their transitivity and expansivity, when the set of configurations is endowed with a shift-invariant (pseudo-)distance. We first give an original proof of the non-transitivity of cellular automata when the set of configurations is endowed with the Besicovitch pseudo-distance. We then show that the Besicovitch pseudo-distance induces a distance on the set of shift-invariant measures and on the whole space of measures, and we prove that in these spaces also, cellular automata cannot be expansive nor transitive.

• Type: Conference
• Year: 2007
• Where: DLT
• Authors: Laurent Bienvenu, Mathieu Sablik
• Keywords: Besicovitch Pseudo-distance, Cellular Automata, DLT 2007, Original Proof, Theoretical Computer Science