A Krieger Embedding Theorem for Near Markov Sofic Shifts

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.