Abstract: A synchronizing automaton is said to be quasi-trapped if it is neither trapped nor strongly connected. Let A be a quasi trapped synchronizing automaton. By using the number of the states of the strongly connected sulrautomaton of A,a upper bound of the length of the shortest synchronizing word of A was given,and then a sufficient condition for A to satisfy the Cerny Conjecture was obtained.

Key words: Quasi trapped synchronizing automaton, Trapped synchronizing automaton, Shortest synchronizing word,Strongly conncctcd sub-automaton,}crny conjccturc