Domino Problem Under Horizontal Constraints

Nathalie Aubrun, Julien Esnay & Mathieu Sablik
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...
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