A word w over a *nite alphabet is said to be n-collapsing if for an arbitrary *nite automaton A = 〈Q; −·−〉, the inequality |Q ·w|6 |Q| − n holds provided that |Q · u|6 |Q| − n for some word u (depending on A). We give an algorithm to test whether a word is 2-collapsing. To this aim we associate to every word w a *nite family of *nitely generated subgroups in *nitely generated free groups and pr...
