Decision problems on geometric tilings
Abstract
We study decision problems on geometric tilings. First, we study a variant of the Domino problem where square tiles are replaced by geometric tiles of arbitrary shape. We show that this variant is undecidable regardless of the shapes, extending the results of [1] on rhombus tiles. This result holds even when the geometric tiling is forced to belong to a fixed set. Second, we consider the problem of deciding whether a geometric subshift has finite local complexity, which is a common assumption when studying geometric tilings. We show that this problem is undecidable even in a simple setting (square shapes with small modifications).
Fields of Study & Subjects
semigroups and automata theory
Computability
Logic
AI Algorithms
Cellular Automata and Applications
Publication details
- Journal / source
- Theoretical Computer Science
- Volume
- 1067
- Pages
- 115756–115756
- Publication date
- 17 January 2026
- Language
- EN