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Permutive One-Way Cellular Automata and the Finiteness Problem for Automaton Groups

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Unveiling Dynamics and Complexity (CiE 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10307))

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Abstract

The decidability of the finiteness problem for automaton groups is a well-studied open question on Mealy automata. We connect this question of algebraic nature to the periodicity problem of one-way cellular automata, a dynamical question known to be undecidable in the general case. We provide a first undecidability result on the dynamics of one-way permutive cellular automata, arguing in favor of the undecidability of the finiteness problem for reset Mealy automata.

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Authors and Affiliations

  1. Univ. Orléans, LIFO EA 4022, 45067, Orléans, France

    Martin Delacourt & Nicolas Ollinger

Authors
  1. Martin Delacourt
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  2. Nicolas Ollinger
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Correspondence to Martin Delacourt .

Editor information

Editors and Affiliations

  1. University of Turku, Turku, Finland

    Jarkko Kari

  2. Christian-Albrechts-University of Kiel, Kiel, Germany

    Florin Manea

  3. Åbo Akademi University, Turku, Finland

    Ion Petre

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Delacourt, M., Ollinger, N. (2017). Permutive One-Way Cellular Automata and the Finiteness Problem for Automaton Groups. In: Kari, J., Manea, F., Petre, I. (eds) Unveiling Dynamics and Complexity. CiE 2017. Lecture Notes in Computer Science(), vol 10307. Springer, Cham. https://doi.org/10.1007/978-3-319-58741-7_23

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  • DOI: https://doi.org/10.1007/978-3-319-58741-7_23

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-58740-0

  • Online ISBN: 978-3-319-58741-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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