Cellular Automata, Decidability and Phasespace

Abstract. Cellular automata have rich computational properties and, at the same time, provide plausible models of physics-like computation. We study decidability issues in the phasespace of these automata, construed as automatic structures over infinite words. In dimension one, slightly more than the first order theory is decidable but the addition of an orbit predicate results in undecidability. We comment on connections between this "what you see is what you get" model and the lack of natural intermediate degrees.

• Type: Journal
• Year: 2010
• Where: FUIN
• Authors: Klaus Sutner
• Keywords: Cellular Automata, FUIN 2010, Natural Intermediate Degrees, Rich Computational Properties