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Pré-Publication, Document De Travail Année : 2013

mu-Limit Sets of Cellular Automata from a Computational Complexity Perspective

Résumé

This paper is about μ-limit sets of cellular automata, i.e. sets of configurations made of words which have a positive probability to appear arbitrarily late in the evolution, starting from an initial μ-random confi guration. More precisely, we investigate the computational complexity of these sets and of decision problems concerning them. Our main results are: fi rst, that such a set can have a Σ_3-hard language, second that it can contain only α-complex confi gurations and third that any non-trivial property concerning these sets is at least Π_3-hard. We also prove various complexity upper bounds, study some restriction of these questions to particular classes of cellular automata, and study di fferent types of (non-)convergence of the probability of appearance of a word in the evolution.
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Dates et versions

hal-00866094 , version 1 (25-09-2013)
hal-00866094 , version 2 (19-06-2015)

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Laurent Boyer, Martin Delacourt, Victor Poupet, Mathieu Sablik, Guillaume Theyssier. mu-Limit Sets of Cellular Automata from a Computational Complexity Perspective. 2013. ⟨hal-00866094v1⟩
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