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Journal of Automata, Languages and Combinatorics - Special issue: Selected papers of the fourth international workshop on descriptional complexity of formal systems
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Unambiguous finite automata over a unary alphabet
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DCFS'12 Proceedings of the 14th international conference on Descriptional Complexity of Formal Systems
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We resolve an open problem raised by Ravikumar and Ibarra [SIAM J. Comput., 18 (1989), pp. 1263--1282] on the succinctness of representations relating to the types of ambiguity of finite automata. We show that there exists a family of nondeterministic finite automata {An} over a two-letter alphabet such that, for any positive integer n, An is exponentially ambiguous and has n states, whereas the smallest equivalent deterministic finite automaton has 2n states, and any smallest equivalent polynomially ambiguous finite automaton has 2n -1 states.