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arXiv · 1808.04925

Complexity of Shift Spaces on Semigroups

J. C. Ban·C. H. Chang·Y. Z. Huang
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Abstract

Let $G=\left\langle S|R_{A}\right\rangle $ be a semigroup with generating set $ S$ and equivalences $R_{A}$ among $S$ determined by a matrix $A$. This paper investigates the complexity of $G$-shift spaces by yielding the topological entropies. After revealing the existence of topological entropy of $G$-shift of finite type ($G$-SFT), the calculation of topological entropy of $G$-SFT is equivalent to solving a system of nonlinear recurrence equations. The complete characterization of topological entropies of $G$-SFTs on two symbols is addressed, which extends [Ban and Chang, arXiv:1803.03082] in which $G$ is a free semigroup.

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J. C. Ban, C. H. Chang, Y. Z. Huang. 2018-08-14. Complexity of Shift Spaces on Semigroups. https://arxiv.org/abs/1808.04925

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