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

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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. © 2011 Springer-Verlag.

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Delacourt, M. (2011). Rice’s theorem for μ-limit sets of cellular automata. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6756 LNCS, pp. 89–100). https://doi.org/10.1007/978-3-642-22012-8_6

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