Simulations Between Cellular Automata on Cayley Graphs.

(eng) We consider cellular automata on Cayley graphs and compare their computational powers according to the architecture on which they work. We show that, if there exists a homomorphism with a finite kernel from a group into another one such that the image of the first group has a finite index in the second one, then every cellular automaton on the Cayley graph of one of these groups can be uniformally simulated by a cellular automaton on the Cayley graph of the other one. This simulation can be constructed in a linear time. With the help of this result we also show that cellular automata working on any Archimedean tiling can be simulated by a cellular automaton on the grid of Z^2 and conversely