Domino Problem Under Horizontal Constraints
Abstract
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 DPH : given a vertical constraint, is it possible to tile the plane? We characterize the nearest-neighbor horizontal constraints where DPH is decidable using graphs combinatorics.
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