Efficient construction of semilinear representations of languages accepted by unary NFA

Authors:
Zdeněk Sawa
Affiliations:
Center for Applied Cybernetics, Department of Computer Science, Technical University of Ostrava, Ostrava-Poruba, Czech republic
Venue:
RP'10 Proceedings of the 4th international conference on Reachability problems
Year:
2010

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Abstract

Chrobak (1986) proved that a language accepted by a given nondeterministic finite automaton with one-letter alphabet, i.e., a unary NFA, with n states can be represented as the union of O(n2) arithmetic progressions, and Martinez (2002) has shown how to compute these progressions in polynomial time. To (2009) has pointed out recently that Chrobak's construction and Martinez's algorithm, which is based on it, contain a subtle error and has shown how they can be corrected. In this paper, a new simpler and more efficient algorithm for the same problem is presented. The running time of the presented algorithm is O(n2(n+m)), where n is the number of states and m the number of transitions of a given unary NFA.