Unitary monoid with two generators: An algorithmic point of view

Abstract

We consider the following problem: Instance: a finite alphabet A, a biprefix code X={x, y} whose elements are primitive, weA*. Question: find every maximal factors of w which are prefixes of a word of X*. We present an algorithm which solves the problem in time linear of the length of w, after a preprocessing phase applied to the set X.