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Computability of Extender Sets in Multidimensional Subshifts

Authors Antonin Callard , Léo Paviet Salomon , Pascal Vanier

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Author Details

Antonin Callard
  • Normandie Univ, UNICAEN, ENSICAEN, CNRS, GREYC, 14000, Caen, France
Léo Paviet Salomon
  • Université de Lorraine, CNRS, Inria, LORIA, 54000, Nancy, France
Pascal Vanier
  • Normandie Univ, UNICAEN, ENSICAEN, CNRS, GREYC, 14000, Caen, France

Funding

This research was partially funded by ANR JCJC 2019 19-CE48-0007-01.

Acknowledgements

We are thankful to the referees for their many helpful remarks and suggestions.

Cite As Get BibTex

Antonin Callard, Léo Paviet Salomon, and Pascal Vanier. Computability of Extender Sets in Multidimensional Subshifts. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 21:1-21:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.STACS.2025.21

Abstract

Subshifts are sets of colorings of ℤ^d defined by families of forbidden patterns. Given a subshift and a finite pattern, its extender set is the set of admissible completions of this pattern. It has been conjectured that the behavior of extender sets, and in particular their growth called extender entropy [French and Pavlov, 2019], could provide a way to separate the classes of sofic and effective subshifts. We prove here that both classes have the same possible extender entropies: exactly the Π₃ real numbers of [0,+∞).

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Discrete mathematics
  • Theory of computation → Models of computation
Keywords
  • Symbolic dynamics
  • subshifts
  • extender sets
  • extender entropy
  • computability
  • sofic shifts
  • tilings

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References

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