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 [(J. Comput. System Sci. 24 (1982) 233; Theoret. Comput. Sci. 72 (1990) 27; Theoret. Comput. Sci. 233 (2000) 19)]. The distance of a DA can be limited or unbounded. Given that the distance of a DA is limited, Hashiguchi has proved in Hashiguchi (2000) that the distance of the automaton is bounded by 24n3+n lg(n+2)+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 23n3+n lg n+n-1.

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