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dc.contributor.advisorRuškuc, Nik
dc.contributor.advisorNeunhöffer, Max
dc.contributor.authorPfeiffer, Markus Johannes
dc.description.abstractThe word problem of a finitely generated group is commonly defined to be a formal language over a finite generating set. The class of finite groups has been characterised as the class of finitely generated groups that have word problem decidable by a finite state automaton. We give a natural generalisation of the notion of word problem from finitely generated groups to finitely generated semigroups by considering relations of strings. We characterise the class of finite semigroups by the class of finitely generated semigroups whose word problem is decidable by finite state automata. We then examine the class of semigroups with word problem decidable by asynchronous two tape finite state automata. Algebraic properties of semigroups in this class are considered, towards an algebraic characterisation. We take the next natural step to further extend the classes of semigroups under consideration to semigroups that have word problem decidable by a finite collection of asynchronous automata working independently. A central tool used in the derivation of structural results are so-called iteration lemmas. We define a hierarchy of the considered classes of semigroups and connect our original results with previous research.en_US
dc.publisherUniversity of St Andrews
dc.rightsCreative Commons Attribution 3.0 Unported
dc.subject.lcshWord problems (Mathematics)en_US
dc.subject.lcshIterative methods (Mathematics)en_US
dc.titleAdventures in applying iteration lemmasen_US
dc.contributor.sponsorUniversity of St Andrews. School of Mathematics and Statisticsen_US
dc.contributor.sponsorEngineering and Physical Sciences Research Council (EPSRC)en_US
dc.type.qualificationnamePhD Doctor of Philosophyen_US
dc.publisher.institutionThe University of St Andrewsen_US
dc.publisher.departmentSchool of Mathematics and Statisticsen_US

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Creative Commons Attribution 3.0 Unported
Except where otherwise noted within the work, this item's licence for re-use is described as Creative Commons Attribution 3.0 Unported