Simulations between cellular automata on cayley graphs

Abstract

We study cellular automata on Cayley graphs from a computational point of view. We are interested in the following problem: given two Cayley graphs, can every cellular automaton on the first graph be simulated by a cellular automaton on the second one, and conversely? We give a sufficient condition for such a two-way simulation to exist. In particular, we show that cellular automata on any planar, modular graph are equivalent to cellular automata on the grid Z2. We interpret this result in terms of planar parallel machines.