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 $\mathsf{GI}$- and $\mathsf{NP}$-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.

中文翻译：

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k块共轭的计算复杂度

我们考虑与有限类型的子移位之间的共轭相关的几个计算问题，仅限于k块代码：验证提议的k块共轭，确定两个移位是否允许k块共轭，并通过a减小移位的表示大小k块共轭。我们给出了多项式时间算法进行验证，并显示$\mathsf{胃肠道}$-和 $\mathsf{NP}$-分别用于确定共轭和减小表示大小的难度。我们的方法集中于顶点移位之间的1块共轭，从中我们可以概括为k块共轭和边缘移位。我们以几个未解决的问题作为结束。