The Domino Problem is Undecidable on Surface Groups

Authors Nathalie Aubrun, Sebastián Barbieri , Etienne Moutot

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Nathalie Aubrun
  • LIP, ENS de Lyon - CNRS - UCBL - Université de Lyon, France
Sebastián Barbieri
  • University of British Columbia, Vancouver, Canada
Etienne Moutot
  • LIP, ENS de Lyon - CNRS - UCBL - Université de Lyon, France
  • University of Turku, Finland

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Nathalie Aubrun, Sebastián Barbieri, and Etienne Moutot. The Domino Problem is Undecidable on Surface Groups. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 46:1-46:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


We show that the domino problem is undecidable on orbit graphs of non-deterministic substitutions which satisfy a technical property. As an application, we prove that the domino problem is undecidable for the fundamental group of any closed orientable surface of genus at least 2.

Subject Classification

ACM Subject Classification
  • Theory of computation → Models of computation
  • tilings
  • substitutions
  • SFTs
  • decidability
  • domino problem


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