PreprintCC BY 4.0arXiv
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.
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BibTeX
@misc{marcus2026krieger,
title = {{A Krieger Embedding Theorem for Near Markov Sofic Shifts}},
author = {Brian Marcus and Tom Meyerovitch and Chengyu Wu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.25475},
eprint = {2606.25475},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.25475},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Krieger Embedding Theorem for Near Markov Sofic Shifts
AU - Brian Marcus
AU - Tom Meyerovitch
AU - Chengyu Wu
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2606.25475
UR - https://arxiv.org/abs/2606.25475
AB - 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.
ER -