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Turing Degrees of Limit Sets of Cellular Automata

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Book cover Automata, Languages, and Programming (ICALP 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8573))

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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.

This work was sponsored by grants EQINOCS ANR 11 BS02 004 03 and TARMAC ANR 12 BS02 007 01.

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Authors and Affiliations

  1. Laboratoire d’algorithmique, complexité et logique Université de Paris-Est, LACL, UPEC, France

    Alex Borello, Julien Cervelle & Pascal Vanier

Authors
  1. Alex Borello
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  2. Julien Cervelle
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  3. Pascal Vanier
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Editor information

Editors and Affiliations

  1. Institut für Informatik, Technische Universität München, Boltzmannstrasse 3, 85748, München, Germany

    Javier Esparza

  2. LIAFA, Université Paris Diderot-Paris 7, Case 7014, 75205, Paris Cedex 13, France

    Pierre Fraigniaud

  3. IT University of Copenhagen, Rued Langgaards Vej 7, 2300, Copenhagen, Denmark

    Thore Husfeldt

  4. Department Computer Science, University of Oxford, Wolfson Building, Parks Road, OX1 3QD, Oxford, UK,

    Elias Koutsoupias

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Borello, A., Cervelle, J., Vanier, P. (2014). Turing Degrees of Limit Sets of Cellular Automata. In: Esparza, J., Fraigniaud, P., Husfeldt, T., Koutsoupias, E. (eds) Automata, Languages, and Programming. ICALP 2014. Lecture Notes in Computer Science, vol 8573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43951-7_7

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  • DOI: https://doi.org/10.1007/978-3-662-43951-7_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-43950-0

  • Online ISBN: 978-3-662-43951-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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