Show simple item record

dc.contributor.authorMeleshko, Joseph Victor Fiorillo 20:37:48 (GMT) 20:37:48 (GMT)
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.publisherUniversity of Waterlooen
dc.titleAutomata and Ratio Setsen
dc.typeMaster Thesisen
dc.pendingfalse R. Cheriton School of Computer Scienceen Scienceen of Waterlooen
uws-etd.degreeMaster of Mathematicsen
uws.contributor.advisorShallit, Jeffrey
uws.contributor.affiliation1Faculty of Mathematicsen

Files in this item


This item appears in the following Collection(s)

Show simple item record


University of Waterloo Library
200 University Avenue West
Waterloo, Ontario, Canada N2L 3G1
519 888 4883

All items in UWSpace are protected by copyright, with all rights reserved.

DSpace software

Service outages