The limitedness problem on distance automata: Hashiguchi's method revisited

Hashiguchi has studied the limitedness problem of distance automata (DA) in a series of paper ([3], [6] and [7]). The distance of a DA can be limited or unbounded. Given that the distance of a DA is limited, Hashiguchi has proved in [7] that the distance of the automaton is bounded by 2 3+n , where n is the number of states. In this paper, we study again Hashiguchi’s solution to the limitedness problem. We have made a number of simplification and improvement on Hashiguchi’s method. We are able to improve the upper bound to 2 3+n lgn+n−1.