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2 Fundamenta Informaticae

2 2002

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Effective Simulations on Hyperbolic Networks

Nichitiu C.M., Rémila E.

Fundamenta Informaticae

2002

Vol. 52, nr 1-3

203-231

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.

A Geometrical Hierarchy on Graphs via Cellular Automata

Martin B.

Fundamenta Informaticae

2002

Vol. 52, nr 1-3

157-181

Historically, cellular automata were defined on the lattices \mathbbZn, but the definition can be extended to bounded degree graphs. Given a notion of simulation between cellular automata defined on different structures (namely graphs of automata), we can deduce an order on graphs. In this paper, we link this order to graph properties and explicit the order for most of the common graphs.