Rice's theorem for µ-limit sets of cellular automata

Authors:
Martin Delacourt
Affiliations:
Laboratoire d'Informatique Fondamentale de Marseille, Université de Provence, France
Venue:
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
Year:
2011

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Abstract

Cellular automata are a parallel and synchronous computing model, made of infinitely many finite automata updating according to the same local rule. Rice's theorem states that any nontrivial property over computable functions is undecidable. It has been adapted by Kari to limit sets of cellular automata [7], that is the set of configurations that can be reached arbitrarily late. This paper proves a new Rice theorem for µ-limit sets, which are sets of configurations often reached arbitrarily late.