A Fast Algorithm for Stallings' Folding Process

The main purpose of this is to give an algorithm that quickly performs Stallings’ Folding algorithm for finitely generated subgroups of a free group. First some definitions, motivations and then results. Let Γ be a directed labeled graph with the labels lying in some alphabet X = {x1, x2, . . . , xn}. Such a graph is said to be folded if at each vertex v there is at most one edge with a given label and incidence starting (or terminating) at v. We now state the following topologically flavoured definition.