Two Tiling is Undecidable
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918057818980352 |
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| author | Stade, Jack |
| author_facet | Stade, Jack |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_11628 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Two Tiling is Undecidable Stade, Jack Computational Geometry Combinatorics Metric Geometry 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. |
| title | Two Tiling is Undecidable |
| topic | Computational Geometry Combinatorics Metric Geometry |
| url | https://arxiv.org/abs/2506.11628 |