Abstract:A sofic shift is a shift space consisting of bi-infinite labels of paths from a labelled graph. Being a dynamical system, the distribution of its closed orbits may indicate the complexity of the space. For this purpose, prime orbit and Mertens' orbit counting functions are introduced as a way to describe the growth of the closed orbits. The asymptotic behaviours of these counting functions can be implied from the analiticity of the Artin-Mazur zeta function of the space. Despite having a closed-form expression… Show more
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