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Complexity of Right-Ideal, Prefix-Closed, and Prefix-Free Regular Languages

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dc.contributor.authorBrzozowski, Janusz
dc.contributor.authorSinnamon, Corwin
dc.date.accessioned2017-10-05T16:58:17Z
dc.date.available2017-10-05T16:58:17Z
dc.date.issued2017
dc.description.abstractA language L over an alphabet E is prefix-convex if, for any words x, y, z is an element of Sigma*, whenever x and xyz are in L, then so is xy. Prefix-convex languages include right-ideal, prefix-closed, and prefix-free languages as special cases. We examine complexity properties of these special prefix-convex languages. In particular, we study the quotient/state complexity of boolean operations, product (concatenation), star, and reversal, the size of the syntactic semi group, and the quotient complexity of atoms. For binary operations we use arguments with different alphabets when appropriate; this leads to higher tight upper bounds than those obtained with equal alphabets. We exhibit right-ideal, prefix-closed, and prefix-free languages that meet the complexity bounds for all the measures listed above.en
dc.description.sponsorshipNatural Sciences and Engineering Research Council of Canada [OGP0000871]en
dc.identifier.urihttp://dx.doi.org/10.14232/actacyb.23.1.2017.3
dc.identifier.urihttp://hdl.handle.net/10012/12530
dc.language.isoenen
dc.publisherInstitute of Informatics: University of Szegeden
dc.subjectatomsen
dc.subjectcomplexity of operationsen
dc.subjectprefix-closeden
dc.subjectprefix-convexen
dc.subjectprefix-freeen
dc.subjectquotient complexityen
dc.subjectregular languagesen
dc.subjectright idealsen
dc.subjectstate complexityen
dc.subjectsyntactic semigroupen
dc.subjectunrestricted alphabetsen
dc.titleComplexity of Right-Ideal, Prefix-Closed, and Prefix-Free Regular Languagesen
dc.typeArticleen
dcterms.bibliographicCitationBrzozowski, J. A., & Sinnamon, C. (2017). Complexity of Right-Ideal, Prefix-Closed, and Prefix-Free Regular Languages. Acta Cybernetica, 23(1), 9–41. https://doi.org/10.14232/actacyb.23.1.2017.3en
uws.contributor.affiliation1Faculty of Mathematicsen
uws.contributor.affiliation2David R. Cheriton School of Computer Scienceen
uws.peerReviewStatusRevieweden
uws.scholarLevelFacultyen
uws.typeOfResourceTexten

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