On countable SFT covers of sparse multidimensional shift spaces
Abstract
A multidimensional sofic shift is called countably covered if it has an SFT cover containing only countably many configurations. In contrast to the one-dimensional setting, not all countable sofic shifts are countably covered. We investigate the existence of countable covers for gap width shifts, where the number of nonzero symbols in a configuration is bounded by a function of the minimum distance between two such symbols. As our main results, we characterize those one-dimensional gap width shifts whose two-dimensional lift is a countably covered sofic shift, and show that a large class of two-dimensional gap width shifts are countably covered.
Fields of Study & Subjects
semigroups and automata theory
Cellular Automata and Applications
Mathematical Dynamics and Fractals
Publication details
- Journal / source
- Theoretical Computer Science
- Volume
- 1066
- Pages
- 115755–115755
- Publication date
- 15 January 2026
- Language
- EN