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Turing degrees of limit sets of cellular automata

Abstract : Cellular automata are discrete dynamical systems and a model of computation. The limit set of a cellular automaton consists of the configurations having an infinite sequence of preimages. It is well known that these always contain a computable point and that any non-trivial property on them is undecidable. We go one step further in this article by giving a full characterization of the sets of Turing degrees of cellular automata: they are the same as the sets of Turing degrees of effectively closed sets containing a computable point.
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Submitted on : Saturday, February 15, 2014 - 2:00:57 PM
Last modification on : Friday, October 4, 2019 - 1:13:17 AM
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Alex Borello, Julien Cervelle, Pascal Vanier. Turing degrees of limit sets of cellular automata. ICALP 2014, Jul 2014, Copenhaguen, Denmark. pp.74--85, ⟨10.1007/978-3-662-43951-7_7⟩. ⟨hal-00947323⟩

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