A Krieger Embedding Theorem for Near Markov Sofic Shifts

Brian Marcus; Tom Meyerovitch; Chengyu Wu

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arXiv · 2606.25475

A Krieger Embedding Theorem for Near Markov Sofic Shifts

Brian Marcus·Tom Meyerovitch·Chengyu Wu

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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.

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Brian Marcus, Tom Meyerovitch, Chengyu Wu. 2026-06-24. A Krieger Embedding Theorem for Near Markov Sofic Shifts. https://arxiv.org/abs/2606.25475

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