Communication complexity and intrinsic universality in cellular automata

Let F be a cellular automaton (CA). This paper establishes necessary conditions for F in order to be intrinsically universal. The central idea is to consider the communication complexity of various “canonical problems” related to the dynamics of F. We show that the intrinsic universality of F implies high communication complexity for each of the canonical problems. This result allows us to rule out many CAs from being intrinsically universal: The linear CAs, the expansive CAs, the reversible CAs and the elementary CAs 218, 33 and 94. The notion of intrinsic universality is related to a process by which we change the scale of space-time diagrams. Therefore, in this work we are answering pure dynamical question by using a computational theory. This communication complexity theory, on the other hand, provides a finer tool than the one given by classical computational complexity analysis. In fact, we prove that for two of the canonical problems there exists a CA for which the computa...

• Type: Journal
• Year: 2011
• Where: TCS
• Authors: Eric Goles Chacc, Pierre-Etienne Meunier, Ivan Rapaport, Guillaume Theyssier
• Keywords: Canonical Problems, Communication Complexity, Intrinsic Universality, TCS 2011, Theoretical Computer Science