Computing degree and class degree

Abstract: Let $\pi$ be a factor code from a one dimensional shift of finite type $X$ onto an irreducible sofic shift $Y$. If $\pi$ is finite-to-one then the number of preimages of a typical point in $Y$ is an invariant called the degree of $\pi$. In this paper we present an algorithm to compute this invariant. The generalized notion of the degree when $\pi$ is not limited to finite-to-one factor codes, is called the class degree of $\pi$. The class degree of a code is defined to be the number of transition classes over a typical point of $Y$ and is invariant under topological conjugacy. We show that the class degree is computable.