Before revision:  We provide a constructive nondeterministic algorithm to solve the cutpoint isolation problem, even for exponentially ambiguousPFA, and we also show that the problem is at least NP-hard  .
After revision:  We provide a constructive nondeterministic algorithm to solve the cutpoint isolation problem, even for exponentially ambiguousPFA, and we also show that the problem is at least NP-hard and use our decision procedure to solve several related problems .