Polynomial-time algorithm for fixed points of nontrivial morphisms

A word ww is a fixed point of a nontrivial morphism hh if w=h(w)w=h(w) and hh is not the identity on the alphabet of ww. The paper presents the first polynomial algorithm deciding whether a given finite word is such a fixed point. The algorithm also constructs the corresponding morphism, which has the smallest possible number of non-erased letters.