English

The Domino problem is undecidable on every rhombus subshift

Discrete Mathematics 2023-08-03 v1

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 Π10\Pi^0_1 -hard and therefore undecidable. It is Π10\Pi^0_1 -complete when the subshift X is given by a computable sequence of forbidden patterns.

Cite

@article{arxiv.2302.12086,
  title  = {The Domino problem is undecidable on every rhombus subshift},
  author = {Benjamin Hellouin de Menibus and Victor H. Lutfalla and Camille Noûs},
  journal= {arXiv preprint arXiv:2302.12086},
  year   = {2023}
}

Comments

12 pages + 1 page of appendix

R2 v1 2026-06-28T08:48:00.178Z