A new algorithm for finding the Shannon cover of shifts of finite type

A shift of finite type (SFT) is a shift space whose constraints can be represented by a finite list of forbidden words. The deterministic labeled graph with the fewest vertices presenting an irreducible SFT (called the Shannon cover) is obtained, in general, via a two-step procedure: The first step is to generate an initial deterministic presentation, and the second one is to apply a vertex-minimization algorithm to identify classes of equivalent vertices. We propose in this paper an algorithm to generate the Shannon cover of a SFT that firstly identify classes of follower set equivalent words derived from the collection of all first offenders. This identification is not based on the allowable sequences obtained from an initial presentation, as is usually done. Having defined the equivalence classes (or the vertices of the minimal presentation) we apply a procedure to connect the vertices and label the edges that yields the essential component of the follower set graph of the SFT.