Effective simulations on hyperbolic networks
We state a definition of the simulation of graph automata, which are machines built by putting copies of the same finite-state automaton at the vertices of a regular graph, reading the states of the neighbors. We first 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.
simulation graph automata cellular automata cayley graphs hyperbolic graphs