Turing degrees of limit sets of cellular automata
Formal Languages and Automata Theory
2014-02-18 v1 Cellular Automata and Lattice Gases
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.
Keywords
Cite
@article{arxiv.1402.3766,
title = {Turing degrees of limit sets of cellular automata},
author = {Alex Borello and Julien Cervelle and Pascal Vanier},
journal= {arXiv preprint arXiv:1402.3766},
year = {2014}
}