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A duality theoretic perspective on recognisable languages

dc.contributor.advisorRewitzky, I. M.en_ZA
dc.contributor.authorRozanova, Juliaen_ZA
dc.contributor.otherStellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Division Mathematics.en_ZA
dc.date.accessioned2019-02-18T09:50:19Z
dc.date.accessioned2019-04-17T08:13:42Z
dc.date.available2019-02-18T09:50:19Z
dc.date.available2019-04-17T08:13:42Z
dc.date.issued2019-04
dc.identifier.urihttp://hdl.handle.net/10019.1/105807
dc.descriptionThesis (MSc)--Stellenbosch University, 2019.en_ZA
dc.description.abstractENGLISH ABSTRACT : A connection between recognisable languages and profinite identities is established through the composition of two famous theorems: Eilenberg’s theorem and Reiterman’s theorem. In this work, we present a detailed account of the duality-theoretic approach by Gehrke et al. that has been shown to bridge the gap and demonstrate that Eilenberg’s varieties and profinite theories are directly linked: they are at opposite ends of an extended Stone-type duality, instantiating a Galois correspondence between subobjects and quotients and resulting in an equational theory of recognisable languages. We give an indepth overview of relevant components of algebraic language theory and the profinite equational theory of pseudovarieties in order to show how they are tied together by the duality-theoretic developments. Furthermore, we provide independent proofs of the key Galois connections at the heart of these bridging results.en_ZA
dc.description.abstractAFRIKAANSE OPSOMMING : Geen Afrikaanse opsomming geskikbaar nieaf_ZA
dc.format.extentvii, 78 pages : illustrationsen_ZA
dc.language.isoen_ZAen_ZA
dc.publisherStellenbosch : Stellenbosch Universityen_ZA
dc.subjectBoolean algebrasen_ZA
dc.subjectFormal language theoryen_ZA
dc.subjectDuality theory (Mathematics)en_ZA
dc.subjectLatticesen_ZA
dc.subjectStone duality (Mathematics)en_ZA
dc.subjectUCTDen_ZA
dc.titleA duality theoretic perspective on recognisable languagesen_ZA
dc.typeThesisen_ZA
dc.rights.holderStellenbosch Universityen_ZA


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