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arXiv · 1909.02627

Computational Complexity of $k$-Block Conjugacy

Tyler Schrock·Rafael Frongillo
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Abstract

We consider several computational problems related to conjugacy between subshifts of finite type, restricted to $k$-block codes: verifying a proposed $k$-block conjugacy, deciding if two shifts admit a $k$-block conjugacy, and reducing the representation size of a shift via a $k$-block conjugacy. We give a polynomial-time algorithm for verification, and show GI and NP-hardness for deciding conjugacy and reducing representation size, respectively. Our approach focuses on 1-block conjugacies between vertex shifts, from which we generalize to $k$-block conjugacies and to edge shifts. We conclude with several open problems.

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Tyler Schrock, Rafael Frongillo. 2019-09-05. Computational Complexity of $k$-Block Conjugacy. https://arxiv.org/abs/1909.02627

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