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 Petersen–Salama entropies [defined in Petersen and Salama (Theoret Comput Sci 743:64–71, 2018)]. After revealing the existence of Petersen–Salama entropy of G-shift of finite type (G-SFT), the calculation of Petersen–Salama entropy of G-SFT is equivalent to solving a system of nonlinear recurrence equations. The complete characterization of Petersen–Salama entropies of G-SFTs on two symbols is addressed, which extends (Ban and Chang in On the topological entropy of subshifts of finite type on free semigroups, 2018. arXiv:1702.04394) in which G is a free semigroup.

令\（G = \ left \ langle S | R_ {A} \ right \ rangle \）是一个半群，具有生成集S和等式\（R_ {A} \）在由矩阵A确定的S中。本文通过产生Petersen-Salama熵[在Petersen和Salama中定义（Theoret Comput Sci 743：64-71，2018）]研究了G移位空间的复杂性。揭示的消弧线萨拉马熵的存在后ģ -Shift有限类型的（g ^ -SFT）的消弧线萨拉马熵的计算ģ -SFT相当于求解非线性复发方程的系统。G的Petersen-Salama熵的完整表征解决了两个符号上的-SFTs，其扩展了（关于自由半群上有限类型的子移位的拓扑熵，Ban和Chang，2018年。arXiv：1702.04394），其中G是自由半群。