Work

On countable SFT covers of sparse multidimensional shift spaces

Year: 2026

Type: article

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.

Source: Theoretical Computer Science

DOI: 10.1016/j.tcs.2026.115755

Author: Ilkka Törmä

Institution: University of Turku

Language: English

Topic: semigroups and automata theory

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,880

Funder: Luonnontieteiden ja Tekniikan Tutkimuksen Toimikunta