Domino Problem Under Horizontal Constraints

Authors Nathalie Aubrun, Julien Esnay, Mathieu Sablik

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Author Details

Nathalie Aubrun
  • Univ Lyon, CNRS, ENS de Lyon, Université Claude Bernard Lyon 1, LIP, F-69342, LYON Cedex 07, France
Julien Esnay
  • Institut de Mathématiques de Toulouse, Université Paul Sabatier, 118 route de Narbonne, F-31062 Toulouse Cedex 9, France
  • Univ Lyon, CNRS, ENS de Lyon, Université Claude Bernard Lyon 1, LIP, F-69342, Lyon Cedex 07, France
Mathieu Sablik
  • Institut de Mathématiques de Toulouse, Université Paul Sabatier, 118 route de Narbonne, F-31062 Toulouse Cedex 9, France

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Nathalie Aubrun, Julien Esnay, and Mathieu Sablik. Domino Problem Under Horizontal Constraints. In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 26:1-26:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


The Domino Problem on ℤ² asks if it is possible to tile the plane with a given set of Wang tiles; it is a classical decision problem which is known to be undecidable. The purpose of this article is to parameterize this problem to explore the frontier between decidability and undecidability. To do so we fix some horizontal constraints H on the tiles and consider a new Domino Problem DP_H: given a vertical constraint, is it possible to tile the plane? We characterize the nearest-neighbor horizontal constraints where DP_H is decidable using graphs combinatorics.

Subject Classification

ACM Subject Classification
  • Theory of computation → Models of computation
  • Mathematics of computing → Combinatoric problems
  • Dynamical Systems
  • Symbolic Dynamics
  • Subshifts
  • Wang tiles
  • Undecidability
  • Domino Problem
  • Combinatorics
  • Tilings
  • Subshifts of Finite Type


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