2018/03/08 by Jung‐Chao Ban, Ban, Jung-Chao, Chih-Hung Chang +1 · 1 citation
Computer Science · Mathematics · #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1803.03082
openalex publication_date 2018/03/08 · openalex created_date 2018/03/29 · openalex updated_date 2026/07/28
In this paper, we provide an effective method to compute the topological entropies of G-subshifts of finite type (G-SFTs) with G=Fd and Sd, the free group and free semigroup with d generators respectively. We develop the entropy formula by analyzing the corresponding systems of nonlinear recursive equations (SNREs). Four types of SNREs of S2-SFTs, namely the types E,D,C and O, are introduced and we could compute their entropies explicitly. This enables us to give the complete characterization of S2-SFTs on two symbols. That is, the set of entropies of S2-SFTs on two symbols is equal to E∪ D∪ C∪ O. The methods developed in Sd-SFTs will also be applied to the study of the entropy theory of Fd-SFTs. The entropy formulae of Sd-, Fd-golden mean shifts and k-colored chessboards are also presented herein.