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dc.contributor.authorBrzozowski, Janusz
dc.contributor.authorLi, Baiyu
dc.contributor.authorLiu, David 22:52:29 (GMT) 22:52:29 (GMT)
dc.description© Otto-von-Guericke-Universit¨at Magdeburg. This is an accepted manuscript. Details about the final published version are available here:
dc.description.abstractThe syntactic complexity of a regular language is the cardinality of its syntactic semi-group. The syntactic complexity of a subclass of regular languages is the maximal syntactic complexity of languages in that subclass, taken as a function of the state complexity n of these languages. We study the syntactic complexity of six subclasses of star-free languages. We find a tight upper bound of (n−1)! for finite/cofinite and re-verse definite languages, and a lower bound of ⌊e·(n−1)!⌋ for definite languages, where e is the base of the natural logarithms. We also find tight upper bounds for languages accepted by monotonic, partially monotonic and “nearly monotonic” automata. All these bounds are significantly lower than the bound nn for arbitrary regular languages. Also, witness languages reaching these bounds require alphabets that grow with n. The syntactic complexity of arbitrary star-free languages remains open.en
dc.description.sponsorshipNatural Sciences and Engineering Research Council of Canada [OGP0000871]en
dc.publisherOtto-von-Guericke-Universit¨at Magdeburgen
dc.subjectcofinite languageen
dc.subjectdefinite languageen
dc.subjectfinite automatonen
dc.subjectfinite languageen
dc.subjectmonotonic automatonen
dc.subjectpartially monotonic automatonen
dc.subjectreverse definite languageen
dc.subjectstar-free languageen
dc.subjectsyntactic complexityen
dc.subjectsyntactic semigroupen
dc.titleSyntactic Complexities of Six Classes of Star-Free Languagesen
dcterms.bibliographicCitationBrzozowski, J., Li, B., & Liu, D. (2012). Syntactic Complexities of Six Classes of Star-Free Languages. Journal of Automata, Languages and Combinatorics, 17(2–4), 83–105.en
uws.contributor.affiliation1Faculty of Mathematicsen
uws.contributor.affiliation2David R. Cheriton School of Computer Scienceen

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