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dc.contributor.advisorRuškuc, Nik
dc.contributor.advisorRoney-Dougal, Colva Mary
dc.contributor.authorBourne, Thomas
dc.coverage.spatialvii, 93 p.en_US
dc.date.accessioned2017-11-07T14:16:13Z
dc.date.available2017-11-07T14:16:13Z
dc.date.issued2017-12-07
dc.identifier.urihttp://hdl.handle.net/10023/12024
dc.description.abstractThe Generalised Star-Height Problem is an open question in the field of formal language theory that concerns a measure of complexity on the class of regular languages; specifically, it asks whether or not there exists an algorithm to determine the generalised star-height of a given regular language. Rather surprisingly, it is not yet known whether there exists a regular language of generalised star-height greater than one. Motivated by a theorem of Thérien, we first take a combinatorial approach to the problem and consider the languages in which every word features a fixed contiguous subword an exact number of times. We show that these languages are all of generalised star-height zero. Similarly, we consider the languages in which every word features a fixed contiguous subword a prescribed number of times modulo a fixed number and show that these languages are all of generalised star-height at most one. Using these combinatorial results, we initiate work on identifying the generalised star-height of the languages that are recognised by finite semigroups. To do this, we establish the generalised star-height of languages recognised by Rees zero-matrix semigroups over nilpotent groups of classes zero and one before considering Rees zero-matrix semigroups over monogenic semigroups. Finally, we explore the generalised star-height of languages recognised by finite groups of a given order. We do this through the use of finite state automata and 'count arrows' to examine semidirect products of the form 𝐴 ⋊ ℤ[sub]𝑟, where 𝐴 is an abelian group and ℤ[sub]𝑟 is the cyclic group of order 𝑟.en_US
dc.language.isoenen_US
dc.publisherUniversity of St Andrews
dc.subjectRegular languageen_US
dc.subjectGeneralised star-heighten_US
dc.subjectSemigroupen_US
dc.subjectMonoiden_US
dc.subjectSubwordsen_US
dc.subject.lccQA267.3B78
dc.subject.lcshFormal languagesen
dc.titleCounting subwords and other results related to the generalised star-height problem for regular languagesen_US
dc.typeThesisen_US
dc.contributor.sponsorEngineering and Physical Sciences Research Council (EPSRC)en_US
dc.type.qualificationlevelDoctoralen_US
dc.type.qualificationnamePhD Doctor of Philosophyen_US
dc.publisher.institutionThe University of St Andrewsen_US


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