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dc.contributor.authorBrzozowski, Janusz
dc.contributor.authorSzykula, Marek
dc.date.accessioned2017-09-29 14:03:06 (GMT)
dc.date.available2017-09-29 14:03:06 (GMT)
dc.date.issued2015-11-01
dc.identifier.urihttp://dx.doi.org/10.1142/S0129054115400067
dc.identifier.urihttp://hdl.handle.net/10012/12507
dc.descriptionElectronic version of an article published as: International Journal of Foundations of Computer Science, 26(07), 2015, 913–931. http://dx.doi.org/10.1142/S0129054115400067 © World Scientific Publishing Company http://www.worldscientific.com/en
dc.description.abstractWe search for the largest syntactic semigroups of star-free languages having n left quotients; equivalently, we look for the largest transition semigroups of aperiodic finite automata with n states. We first introduce unitary semigroups generated by transformations that change only one state. In particular, we study unitary-complete semigroups which have a special structure, and show that each maximal unitary semigroup is unitary-complete. For n >= 4 we exhibit a unitary-complete semigroup that is larger than any aperiodic semigroup known to date. We then present even larger aperiodic semigroups, generated by transformations that map a non-empty subset of states to a single state; we call such transformations and semigroups semiconstant. We examine semiconstant tree semigroups which have a structure based on full binary trees. The semiconstant tree semigroups are at present the best candidates for largest aperiodic semigroups.en
dc.description.sponsorshipNatural Sciences and Engineering Research Council of Canada [OGP000087]en
dc.description.sponsorshipPolish MNiSZW [IP2012 052272]en
dc.language.isoenen
dc.publisherWorld Scientific Publishingen
dc.subjectAperiodicen
dc.subjectmonotonicen
dc.subjectsemiconstanten
dc.subjecttransition semigroupen
dc.subjectstar-free languageen
dc.subjectsyntactic complexityen
dc.subjectunitary.en
dc.titleLarge Aperiodic Semigroupsen
dc.typeConference Paperen
dcterms.bibliographicCitationBrzozowski, J., & Szykuła, M. (2015). Large Aperiodic Semigroups. International Journal of Foundations of Computer Science, 26(07), 913–931. https://doi.org/10.1142/S0129054115400067en
uws.contributor.affiliation1Faculty of Mathematicsen
uws.contributor.affiliation2David R. Cheriton School of Computer Scienceen
uws.typeOfResourceTexten
uws.peerReviewStatusRevieweden
uws.scholarLevelFacultyen


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