Computational Complexity of k-Block Conjugacy

09/05/2019

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by   Tyler Schrock, et al.

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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.