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Cellular Automata: Real-Time Equivalence Between One-Dimensional Neighborhoods

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STACS 2005 (STACS 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3404))

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Abstract

It is well known that one-dimensional cellular automata working on the usual neighborhood are Turing complete, and many acceleration theorems are known. However very little is known about the other neighborhoods. In this article, we prove that every one-dimensional neighborhood that is sufficient to recognize every Turing language is equivalent (in terms of real-time recognition) either to the usual neighborhood {–1,0,1} or to the one-way neighborhood {0,1}.

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Author information

Authors and Affiliations

  1. LIP (UMR CNRS, ENS Lyon, INRIA, Univ. Claude Bernard Lyon 1), École Normale Supérieure de Lyon, 46 allée d’Italie, 69364 cedex 07, LYON, France

    Victor Poupet

Authors
  1. Victor Poupet
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Editor information

Editors and Affiliations

  1. Universität Stuttgart, FMI, Germany

    Volker Diekert

  2. LIF, CNRS & Univ. de Provence,, Marseille

    Bruno Durand

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© 2005 Springer-Verlag Berlin Heidelberg

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Poupet, V. (2005). Cellular Automata: Real-Time Equivalence Between One-Dimensional Neighborhoods. In: Diekert, V., Durand, B. (eds) STACS 2005. STACS 2005. Lecture Notes in Computer Science, vol 3404. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31856-9_11

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  • DOI: https://doi.org/10.1007/978-3-540-31856-9_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24998-6

  • Online ISBN: 978-3-540-31856-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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