English

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}
}