A new dimension sensitive property for cellular automata

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 sensi...

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Veröffentlicht in:	Theoretical computer science 2005-11, Vol.345 (2), p.235-247
Hauptverfasser:	Bernardi, Vincent, Durand, Bruno, Formenti, Enrico, Kari, Jarkko
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Applied sciences Automata. Abstract machines. Turing machines Computer science control theory systems Exact sciences and technology Mathematics Number theory Number-conserving cellular automata Number-decreasing cellular automata Sciences and techniques of general use Theoretical computing Undecidability
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Zusammenfassung:	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.
ISSN:	0304-3975 1879-2294
DOI:	10.1016/j.tcs.2005.07.009