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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Communication dans un congrès
ICALP 2014, Jul 2014, Copenhaguen, Denmark. Automata, Languages, and Programming - 41st International Colloquium, ICALP 2014, Copenhagen, Denmark, July 8-11, 2014, Proceedings, Part II, pp.74--85, 2014, 〈10.1007/978-3-662-43951-7_7〉
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Soumis le : samedi 15 février 2014 - 14:00:57
Dernière modification le : mercredi 20 juin 2018 - 14:18:42
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Alex Borello, Julien Cervelle, Pascal Vanier. Turing degrees of limit sets of cellular automata. ICALP 2014, Jul 2014, Copenhaguen, Denmark. Automata, Languages, and Programming - 41st International Colloquium, ICALP 2014, Copenhagen, Denmark, July 8-11, 2014, Proceedings, Part II, pp.74--85, 2014, 〈10.1007/978-3-662-43951-7_7〉. 〈hal-00947323〉

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