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.