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dc.contributor.authorLiu, Bo Yang Victor
dc.contributor.authorDavies, Sylvie
dc.contributor.authorBrzozowski, Janusz
dc.date.accessioned2017-11-13 22:52:27 (GMT)
dc.date.available2017-11-13 22:52:27 (GMT)
dc.date.issued2016-10-17
dc.identifier.other1511.00157v3
dc.identifier.urihttp://hdl.handle.net/10012/12623
dc.description.abstractA right ideal (left ideal, two-sided ideal) is a non-empty language $L$ over an alphabet $\Sigma$ such that $L=L\Sigma^*$ ($L=\Sigma^*L$, $L=\Sigma^*L\Sigma^*$). Let $k=3$ for right ideals, 4 for left ideals and 5 for two-sided ideals. We show that there exist sequences ($L_n \mid n \ge k $) of right, left, and two-sided regular ideals, where $L_n$ has quotient complexity (state complexity) $n$, such that $L_n$ is most complex in its class under the following measures of complexity: the size of the syntactic semigroup, the quotient complexities of the left quotients of $L_n$, the number of atoms (intersections of complemented and uncomplemented left quotients), the quotient complexities of the atoms, and the quotient complexities of reversal, star, product (concatenation), and all binary boolean operations. In that sense, these ideals are "most complex" languages in their classes, or "universal witnesses" to the complexity of the various operations.en
dc.description.sponsorshipNatural Sciences and Engineering Research Council of Canada [OGP0000871]en
dc.language.isoenen
dc.publisherDiscrete Mathematics and Theoretical Computer Scienceen
dc.rightsAttribution 4.0 International*
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/*
dc.subjectatomen
dc.subjectbasic operationsen
dc.subjectidealen
dc.subjectmost complexen
dc.subjectquotienten
dc.subjectregular languageen
dc.subjectstate complexityen
dc.subjectsyntactic semigroupen
dc.subjectuniversal witnessen
dc.titleMost Complex Regular Ideal Languagesen
dc.typeArticleen
dcterms.bibliographicCitationLiu, B. Y. V., Davies, S., & Brzozowski, J. (2016). Most Complex Regular Ideal Languages. Discrete Mathematics & Theoretical Computer Science, Vol. 18 no. 3. Retrieved from http://dmtcs.episciences.org/2167/pdfen
uws.contributor.affiliation1Faculty of Mathematicsen
uws.contributor.affiliation2David R. Cheriton School of Computer Scienceen
uws.typeOfResourceTexten
uws.peerReviewStatusRevieweden
uws.scholarLevelFacultyen


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