Computing degree and class degree

Let $π$ be a factor code from a one dimensional shift of finite type $X$ onto an irreducible sofic shift $Y$. If $π$ is finite-to-one then the number of preimages of a typical point in $Y$ is an invariant called the degree of $π$. In this paper we present an algorithm to compute this invariant. The generalized notion of the degree when $π$ is not limited to finite-to-one factor codes, is called the class degree of $π$. 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.

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