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Conference on Computability in Europe

CiE 2016: Pursuit of the Universal pp 205–214Cite as

The Domino Problem for Self-similar Structures

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 9709)

Abstract

We define the domino problem for tilings over self-similar structures of \(\mathbb {Z}^d\) given by forbidden patterns. In this setting we exhibit non-trivial families of subsets with decidable and undecidable domino problem.

Keywords

  • Domino Problem
  • Self-similar Substitution
  • Forbidden Patterns
  • Weak Grid
  • Strong Grid

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Acknowledgements

We would like to thank the reviewers for their helpful remarks. This work was partially supported by the ANR project QuasiCool (ANR-12-JS02-011-01)

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Authors and Affiliations

  1. LIP, ENS de Lyon – CNRS – INRIA – UCBL – Université de Lyon, Lyon, France

    Sebastián Barbieri

  2. Institut de Mathmatiques de Marseille, UMR 7373, Aix-Marseille Université, Marseille, France

    Mathieu Sablik

Authors
  1. Sebastián Barbieri
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  2. Mathieu Sablik
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Corresponding author

Correspondence to Sebastián Barbieri .

Editor information

Editors and Affiliations

  1. Swansea University, Swansea, United Kingdom

    Arnold Beckmann

  2. Université Paris-Diderot - Paris 7, Paris, France

    Laurent Bienvenu

  3. University of South Florida, Tampa, Florida, USA

    Nataša Jonoska

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Barbieri, S., Sablik, M. (2016). The Domino Problem for Self-similar Structures. In: Beckmann, A., Bienvenu, L., Jonoska, N. (eds) Pursuit of the Universal. CiE 2016. Lecture Notes in Computer Science(), vol 9709. Springer, Cham. https://doi.org/10.1007/978-3-319-40189-8_21

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  • DOI: https://doi.org/10.1007/978-3-319-40189-8_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40188-1

  • Online ISBN: 978-3-319-40189-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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