A Characterization of Subshifts with Computable Language

Authors Emmanuel Jeandel , Pascal Vanier

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Author Details

Emmanuel Jeandel
  • LORIA, Campus Scientifique - BP 239, 54506 Vandoeuvre-les-Nancy, France
Pascal Vanier
  • Laboratoire d'Algorithmique, Complexité et Logique, Université de Paris-Est, LACL, UPEC, France


The authors wish to thanks the anonymous referees for many helpful remarks and improvements.

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Emmanuel Jeandel and Pascal Vanier. A Characterization of Subshifts with Computable Language. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 40:1-40:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


Subshifts are sets of colorings of Z^d by a finite alphabet that avoid some family of forbidden patterns. We investigate here some analogies with group theory that were first noticed by the first author. In particular we prove several theorems on subshifts inspired by Higman’s embedding theorems of group theory, among which, the fact that subshifts with a computable language can be obtained as restrictions of minimal subshifts of finite type.

Subject Classification

ACM Subject Classification
  • Theory of computation → Models of computation
  • subshifts
  • computability
  • Enumeration degree
  • Turing degree
  • minimal subshifts


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