Effective Simulations on Hyperbolic Networks

. We state a denition of the simulation of graph automata, which are machines built by putting copies of the same nite-state automaton at the vertices of a regular graph, reading the states of the neighbors. We rst present the notion of simulation and link it to intrinsic graph properties. Afterwards, we present some results of simulation between such graph automata, comparing them to the cellular automata on Cayley graphs. The graphs considered here are planar, with the elementary cycles of the same length, and form regular tilings of the hyperbolic plane. We conclude with a possible speed hierarchy. 1 Introduction Since the beginning of the electronic computer era, dierent machine models have existed, but while the classical sequential computer has been enormously developed, the intrinsic massive parallel models had a harder time to get o, maybe because it is more dicult for us to understand the behavior of such tools and to build and steer them correctly. However, several fund..