Year: 2026
Type: preprint
Abstract: Krieger's classical embedding theorem gives necessary and sufficient conditions for embedding a subshift into a mixing shift of finite type (SFT) as a proper subshift. The same result does not hold if one replaces mixing SFT by a mixing sofic shift. In this paper, we generalize Krieger's conditions to give necessary and sufficient conditions for embedding a subshift into a mixing (in fact irreducible) near Markov sofic shift (a special conjugacy-invariant class of sofic shifts). We also show that if the subshift to be embedded is irreducible sofic, then the conditions are finitely decidable.
Source: arXiv (Cornell University)
Authors: Marcus, Brian, Meyerovitch, Tom, Wu, Chengyu
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7165922114