Turing Degrees of Limit Sets of Cellular Automata

  • Alex Borello
  • Julien Cervelle
  • Pascal Vanier
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8573)

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 limit sets of cellular automata: they are the same as the sets of Turing degrees of effectively closed sets containing a computable point.

Keywords

Entropy 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Alex Borello
    • 1
  • Julien Cervelle
    • 1
  • Pascal Vanier
    • 1
  1. 1.Laboratoire d’algorithmiquecomplexité et logique Université de Paris-Est, LACL, UPECFrance

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