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.
https://hal.archives-ouvertes.fr/hal-00947323
Contributor : Pascal Vanier
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Submitted on : Saturday, February 15, 2014 - 2:00:57 PM
Last modification on : Wednesday, June 20, 2018 - 2:18:42 PM
Document(s) archivé(s) le : Thursday, May 15, 2014 - 11:20:52 AM
