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 -hard and therefore undecidable. It is -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