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Slopes of 3-Dimensional Subshifts of Finite Type

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Computer Science – Theory and Applications (CSR 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10846))

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Abstract

In this paper we study the directions of periodicity of three-dimensional subshifts of finite type (SFTs) and in particular their slopes. A configuration of a subshift has a slope of periodicity if it is periodic in exactly one direction, the slope being the angles of the periodicity vector. In this paper, we prove that any \(\varSigma ^0_2\) set may be realized as a a set of slopes of an SFT.

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Acknowledgements

The authors would like to thank anonymous reviewers who pointed out a mistake in a previous version of the paper.

This work was supported by grant TARMAC ANR 12 BS02 007 01.

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Authors and Affiliations

  1. LIP, ENS de Lyon – CNRS – INRIA – UCBL – Université de Lyon, 6 all ée d’Italie, 69364, Lyon Cedex, France

    Etienne Moutot

  2. Laboratoire d’Algorithmique, Complexité et Logique Université de Paris-Est, LACL, UPEC, Paris, France

    Pascal Vanier

Authors
  1. Etienne Moutot
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  2. Pascal Vanier
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Correspondence to Pascal Vanier .

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Editors and Affiliations

  1. Department of Informatics, University of Bergen, Bergen, Norway

    Fedor V. Fomin

  2. Steklov Mathematical Institute, Moscow, Russia

    Vladimir V. Podolskii

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Moutot, E., Vanier, P. (2018). Slopes of 3-Dimensional Subshifts of Finite Type. In: Fomin, F., Podolskii, V. (eds) Computer Science – Theory and Applications. CSR 2018. Lecture Notes in Computer Science(), vol 10846. Springer, Cham. https://doi.org/10.1007/978-3-319-90530-3_22

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  • DOI: https://doi.org/10.1007/978-3-319-90530-3_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-90529-7

  • Online ISBN: 978-3-319-90530-3

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