μ-Limit Sets of Cellular Automata from a Computational Complexity Perspective
Abstract
This paper concerns $\mu$-limit sets of cellular automata: sets of
configurations made of words whose probability to appear does not
vanish with time, starting from an initial $\mu$-random
configuration. More precisely, we investigate the computational
complexity of these sets and of related decision problems. Main
results: first, $\mu$-limit sets can have a $\Sigma_3^0$-hard
language, second, they can contain only $\alpha$-complex
configurations, third, any non-trivial property concerning them is
at least $\Pi_3^0$-hard. We prove complexity upper bounds, study
restrictions of these questions to particular classes of CA, and
different types of (non-)convergence of the measure of a word
during the evolution.
Origin : Files produced by the author(s)
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