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arXiv · 2302.12086

The Domino problem is undecidable on every rhombus subshift

Benjamin Hellouin de Menibus·Victor H. Lutfalla·Camille Noûs
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Abstract

We extend the classical Domino problem to any tiling of rhombus-shaped tiles. For any subshift X of edge-to-edge rhombus tilings, such as the Penrose subshift, we prove that the associated X-Domino problem is $\Pi^0_1$ -hard and therefore undecidable. It is $\Pi^0_1$ -complete when the subshift X is given by a computable sequence of forbidden patterns.

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Benjamin Hellouin de Menibus, Victor H. Lutfalla, Camille Noûs. 2023-02-23. The Domino problem is undecidable on every rhombus subshift. https://doi.org/10.1007/978-3-031-33264-7_9

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