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.
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Zs. Róka. Cellular automata on Cayley graphs. PhD thesis, Ecole Normale Supérieure de Lyon, France, July 1994.
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© 1995 Springer-Verlag Berlin Heidelberg
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Róka, Z. (1995). Simulations between cellular automata on cayley graphs. In: Baeza-Yates, R., Goles, E., Poblete, P.V. (eds) LATIN '95: Theoretical Informatics. LATIN 1995. Lecture Notes in Computer Science, vol 911. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59175-3_112
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DOI: https://doi.org/10.1007/3-540-59175-3_112
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