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Plane-Walking Automata

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Cellular Automata and Discrete Complex Systems (AUTOMATA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8996))

Abstract

In this article, we study classes of multidimensional subshifts defined by multihead finite automata, in particular the hierarchy of classes of subshifts defined as the number of heads grows. The hierarchy collapses on the third level, where all co-recursively enumerable subshifts are obtained in every dimension. We also compare these classes to SFTs and sofic shifts. We are unable to separate the second and third level of the hierarchy in one and two dimensions, and suggest a related open problem for two-counter machines.

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Notes

  1. 1.

    Strictly speaking, they were augmented by markers, but the difference is small.

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Authors and Affiliations

  1. TUCS – Turku Centre for Computer Science, University of Turku, Turku, Finland

    Ville Salo & Ilkka Törmä

Authors
  1. Ville Salo
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  2. Ilkka Törmä
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Corresponding author

Correspondence to Ilkka Törmä .

Editor information

Editors and Affiliations

  1. University of Hyogo, Himeji, Japan

    Teijiro Isokawa

  2. Hiroshima University, Hiroshima, Japan

    Katsunobu Imai

  3. University of Hyogo, Himeji, Japan

    Nobuyuki Matsui

  4. National Institute of Information and Communications Technology, Osaka, Japan

    Ferdinand Peper

  5. Osaka Electro-Communication University, Osaka, Japan

    Hiroshi Umeo

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Salo, V., Törmä, I. (2015). Plane-Walking Automata. In: Isokawa, T., Imai, K., Matsui, N., Peper, F., Umeo, H. (eds) Cellular Automata and Discrete Complex Systems. AUTOMATA 2014. Lecture Notes in Computer Science(), vol 8996. Springer, Cham. https://doi.org/10.1007/978-3-319-18812-6_11

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  • DOI: https://doi.org/10.1007/978-3-319-18812-6_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-18811-9

  • Online ISBN: 978-3-319-18812-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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