A new dimension sensitive property for cellular automata

Authors:
Vincent Bernardi;Bruno Durand;Enrico Formenti;Jarkko Kari
Affiliations:
LIF, CNRS - Université de Provence, Marseille Cedex, France;LIF, CNRS - Université de Provence, Marseille Cedex, France;UNSA - CNRS, Les Algorithmes - bat Euclide B, Sophia Antipolis Cedex, France;Department of Mathematics, University of Turku, Finland
Venue:
Theoretical Computer Science - Mathematical foundations of computer science 2004
Year:
2005

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Abstract

In this paper we study number-decreasing cellular automata. They form a super-class of standard number-conserving cellular automata. It is well-known that the property of being number-conserving is decidable in quasi-linear time. In this paper we prove that being number-decreasing is dimension sensitive, i.e. it is decidable for one-dimensional cellular automata and undecidable for dimension 2 or greater. There are only few known examples of dimension sensitive properties for cellular automata and this denotes some rich panel of phenomena in this class.