dc.contributor.author Meleshko, Joseph Victor Fiorillo dc.date.accessioned 2022-12-13 20:37:48 (GMT) dc.date.available 2022-12-13 20:37:48 (GMT) dc.date.issued 2022-12-13 dc.date.submitted 2022-12-02 dc.identifier.uri http://hdl.handle.net/10012/18952 dc.description.abstract This 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.language.iso en en dc.publisher University of Waterloo en dc.title Automata and Ratio Sets en dc.type Master Thesis en dc.pending false uws-etd.degree.department David R. Cheriton School of Computer Science en uws-etd.degree.discipline Computer Science en uws-etd.degree.grantor University of Waterloo en uws-etd.degree Master of Mathematics en uws-etd.embargo.terms 0 en uws.contributor.advisor Shallit, Jeffrey uws.contributor.affiliation1 Faculty of Mathematics en uws.published.city Waterloo en uws.published.country Canada en uws.published.province Ontario en uws.typeOfResource Text en uws.peerReviewStatus Unreviewed en uws.scholarLevel Graduate en
﻿

### This item appears in the following Collection(s)

UWSpace

University of Waterloo Library
200 University Avenue West