Towards the frontier between decidability and undecidability for hyperbolic cellular automata

Authors:
Maurice Margenstern
Affiliations:
Université Paul Verlaine-Metz, IUT de Metz, LITA EA, UFR MIM, Metz Cédex 1, France
Venue:
RP'10 Proceedings of the 4th international conference on Reachability problems
Year:
2010

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Abstract

In this paper, we look at two ways to implement one dimensional cellular automata into hyperbolic cellular automata in three contexts: the pentagrid, the heptagrid and the dodecagrid, these tilings being classically denoted by {5, 4}, {7, 3} and {5, 3, 4} respectively. As an application, this may give a hint for the boundary between decidable and undecidable problems for hyperbolic cellular automata.