Mortality and Synchronization of Unambiguous Finite Automata
Résumé
We study mortal words and words of minimum non-zero rank (in particular, synchronizing words) in strongly connected unambiguous automata. We show that every n-state strongly connected unambiguous automaton admits a word of minimum non-zero rank of length at most n5 , and this word can be found in polynomial time. We show that for words of minimum rank this upper bound can be lowered to O(n3(logn)4) for prefix automata of finite codes and to O(n3logn) for prefix automata of complete finite codes. We also provide quadratic lower bounds on the length of shortest mortal words for several classes of deterministic automata.