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.

This work was partially supported by the Esprit Basic Research Action “Algebraic and Semantical Methods In Computer Science” and by a Grant of the French Government.