Automata and Ratio Sets

dc.contributor.authorMeleshko, Joseph Victor Fiorillo
dc.date.accessioned2022-12-13T20:37:48Z
dc.date.available2022-12-13T20:37:48Z
dc.date.issued2022-12-13
dc.date.submitted2022-12-02
dc.description.abstractThis thesis explores the composition of ratio sets, the subsets of the rationals derived from the quotients of two sets of natural numbers, and examines a variety of specific examples where the comprising sets of natural numbers have specific properties. I present a general algorithm that decides the inclusion of a rational number in a specific ratio set if the comprising sets of natural numbers are a regular language when represented in a given base. I also present an algorithm for deciding the inclusion of a rational number in the ratio set of a few select sets of natural numbers that are not a regular language when represented in any base, namely, the set of natural numbers with representations in a specific base that are palindromes or antipalindromes. Using those algorithms, I examine some of the rational numbers in specific ratio sets and then prove several results regarding the composition of those ratio sets. As well, I present algorithms for computing approximations to real numbers using elements of some specific ratio sets.en
dc.identifier.urihttp://hdl.handle.net/10012/18952
dc.language.isoenen
dc.pendingfalse
dc.publisherUniversity of Waterlooen
dc.titleAutomata and Ratio Setsen
dc.typeMaster Thesisen
uws-etd.degreeMaster of Mathematicsen
uws-etd.degree.departmentDavid R. Cheriton School of Computer Scienceen
uws-etd.degree.disciplineComputer Scienceen
uws-etd.degree.grantorUniversity of Waterlooen
uws-etd.embargo.terms0en
uws.contributor.advisorShallit, Jeffrey
uws.contributor.affiliation1Faculty of Mathematicsen
uws.peerReviewStatusUnrevieweden
uws.published.cityWaterlooen
uws.published.countryCanadaen
uws.published.provinceOntarioen
uws.scholarLevelGraduateen
uws.typeOfResourceTexten

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