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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

Cellular Automaton Turing Machine Sparse Grid Turing Degree Computation Zone 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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