2025/08/04 by Brian Marcus, Tom Meyerovitch, Marcus, Brian +5 · 1 citation
Computer Science · Engineering · #37B10 (Primary) #Cellular Automata and Applications #Coding theory and cryptography #Dynamical Systems (math.DS) #FOS: Mathematics #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2508.02554
openalex publication_date 2025/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Generalizing a result of MacDonald we give necessary and sufficient conditions for an arbitrary subshift to embed into an irreducible sofic shift factoring through a given cover by an irreducible subshift of finite type (SFT). We obtain also necessary and sufficient conditions for an arbitrary subshift to embed into an irreducible sofic shift factoring through some sliding block code out of an irreducible SFT. We do that when the code is required to be surjective, and hence a factor code, and when it is required to be injective or almost invertible, or is allowed to be arbitrary. These results require concepts of the period of an irreducible sofic shift as well as a concept of a p-periodic subshift. Several equivalent formulations of the period are developed.