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Turing degrees of limit sets of cellular automata

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.

preprint2014arXivOpen access
Alex BorelloJulien CervellePascal Vanier
Formal Languages and Automata Theorynlin.CG
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Alex BorelloJulien CervellePascal Vanier

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