Complexity of Shift Spaces on Semigroups

08/14/2018

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by   J. C. Ban, et al.

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Let G=〈 S|R_A〉 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.