On finite-to-one codes between subshifts

Abstract

Finite equivalence is closely related to finite-to-one codes. To check that given two shift spaces are finitely equivalent we must be able to find a shift of finite type and determine whether a given sliding block code is finite-to-one or not. In this sense finding an equivalent condition for a sliding block code being finite-to-one is important. In this paper we extend the equivalent conditions known for irreducible shifts of finite type to irreducible sofic shifts in domain. Also we generalize the Replacement Theorem to sofic case. Finally by exhibiting finite equivalence between two irreducible edge shifts in detail we apply the method to construct finite equivalence to generalized situation.