A family of NFAs which need 2n - α deterministic states

Authors:
Kazuo Iwama;Akihiro Matsuura;Mike Paterson
Affiliations:
School of Informatics, Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto 606-8501, Japan;School of Informatics, Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto 606-8501, Japan;Department of Computer Science, University of Warwick, Coventry CV4 7AL, UK
Venue:
Theoretical Computer Science
Year:
2003

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Abstract

We show that for all integers n ≥ 7 and α, such that 5 ≤ α ≤ 2n - 2 and satisfying some coprimality conditions, there exists a minimum n-state nondeterministic finite automaton that is equivalent to a minimum deterministic finite automaton with exactly 2n - α states.