Countable Sofic Shifts with a Periodic Direction
Ilkka T\"orm\"a

TL;DR
This paper investigates whether all countable multidimensional sofic shifts have countable SFT covers, providing counterexamples and establishing conditions under which such covers exist.
Contribution
It introduces explicit counterexamples to the equal entropy cover problem and formulates conditions for countable SFT covers in certain shift spaces.
Findings
Counterexamples to the equal entropy cover problem
Necessary and sufficient conditions for countable SFT covers in a restricted class
Identification of limitations in existing cover theories
Abstract
As a variant of the equal entropy cover problem, we ask whether all multidimensional sofic shifts with countably many configurations have SFT covers with countably many configurations. We answer this question in the negative by presenting explicit counterexamples. We formulate necessary conditions for a vertically periodic shift space to have a countable SFT cover, and prove that they are sufficient in a natural (but quite restricted) subclass of shift spaces.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
