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The tractability frontier for NFA minimization
Umeå University, Faculty of Science and Technology, Department of Computing Science. (Formella och naturliga språk)
2012 (English)In: Journal of computer and system sciences (Print), ISSN 0022-0000, E-ISSN 1090-2724, Vol. 78, no 1, p. 198-210Article in journal (Refereed) Published
Abstract [en]

We prove that minimizing finite automata is NP-hard for almost all classes of automata that extend the class of deterministic finite automata. More specifically, we show that minimization is NP-hard for all finite automata classes that subsume the class of δNFAs which accept strings of length at most three. Here, δNFAs are the finite automata that are unambiguous, allow at most one state q with a non-deterministic transition for at most one alphabet symbol a, and are allowed to visit state q at most once in a run. As a corollary, we also obtain that the same result holds for all finite automata classes that subsume that class of finite automata that are unambiguous, have at most two initial states, and accept strings of length at most two.

Place, publisher, year, edition, pages
Elsevier , 2012. Vol. 78, no 1, p. 198-210
Keyword [en]
Finite automata, Optimization, State minimization, Complexity
National Category
Computer Sciences
Identifiers
URN: urn:nbn:se:umu:diva-48008DOI: 10.1016/j.jcss.2011.03.001OAI: oai:DiVA.org:umu-48008DiVA, id: diva2:446104
Available from: 2011-10-06 Created: 2011-10-06 Last updated: 2018-01-12

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Björklund, Henrik
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CiteExportLink to record
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  • apa
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