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arXiv · 2210.08150

Encoding subshifts through sliding block codes

Sophie MacDonald
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Abstract

We prove a generalization of Krieger's embedding theorem, in the spirit of zero-error information theory. Specifically, given a mixing shift of finite type $X$, a mixing sofic shift $Y$, and a surjective sliding block code $\pi: X \to Y$, we give necessary and sufficient conditions for a subshift $Z$ of topological entropy strictly lower than that of $Y$ to admit an embedding $\psi: Z \to X$ such that $\pi \circ \psi$ is injective.

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Sophie MacDonald. 2022-10-15. Encoding subshifts through sliding block codes. https://doi.org/10.1017/etds.2023.56

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