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arXiv · 2506.11628

Two Tiling is Undecidable

Jack Stade
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Abstract

We show that the following problem is undecidable: given two polygonal prototiles, determine whether the plane can be tiled with rotated and translated copies of them. This improves a result of Demaine and Langerman [SoCG 2025], who showed undecidability for three tiles. Along the way, we show that tiling with one prototile is undecidable if there can be edge-to-edge matching rules. This is the first result to show undecidability for monotiling with only local matching constraints.

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Jack Stade. 2025-06-13. Two Tiling is Undecidable. https://arxiv.org/abs/2506.11628

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