Browsing Theses by Supervisor "Shallit, Jeffrey"
Now showing items 1-10 of 10
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Automata and Ratio Sets
(University of Waterloo, 2022-12-13)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 ... -
Counting Flimsy Numbers via Formal Language Theory
(University of Waterloo, 2021-02-02)Let s_2(n) be the sum of the digits of n when expressed in base 2. For integers n and k, Stolarsky defined n to be k-flimsy if s_2(kn) < s_2(n). In this paper, we generalize the definition of k-flimsy numbers to all bases ... -
Counting, Adding, and Regular Languages
(University of Waterloo, 2018-12-17)In this thesis we consider two mostly disjoint topics in formal language theory that both involve the study and use of regular languages. The first topic lies in the intersection of automata theory and additive number ... -
Decision Algorithms for Ostrowski-Automatic Sequences
(University of Waterloo, 2020-05-13)We extend the notion of automatic sequences to a broader class, the Ostrowski-automatic sequences. We develop a procedure for computationally deciding certain combinatorial and enumeration questions about such sequences ... -
Discriminators of Integer Sequences
(University of Waterloo, 2017-08-28)The discriminator of an integer sequence \textbf{s} = $(s(n))_{n \geq 0}$, first introduced by Arnold, Benkoski and McCabe in 1985, is the function $D_s (n)$ that maps the integer $n \geq 1$ to the smallest positive integer ... -
On the Properties and Structure of Bordered Words and Generalizations
(University of Waterloo, 2022-10-12)Combinatorics on words is a field of mathematics and theoretical computer science that is concerned with sequences of symbols called words, or strings. One class of words that are ubiquitous in combinatorics on words, ... -
Powers and Anti-Powers in Binary Words
(University of Waterloo, 2019-08-28)Fici et al. recently introduced the notion of anti-powers in the context of combinatorics on words. A power (also called tandem repeat) is a sequence of consecutive identical blocks. An anti-power is a sequence of consecutive ... -
Properties of Two-Dimensional Words
(University of Waterloo, 2017-04-21)Combinatorics on words in one dimension is a well-studied subfield of theoretical computer science with its origins in the early 20th century. However, the closely-related study of two-dimensional words is not as popular, ... -
Proving Properties of Fibonacci Representations via Automata Theory
(University of Waterloo, 2024-01-22)In this work, we introduce a novel framework for mechanically testing the completeness and unambiguity of Fibonacci-based representations via automata theory. We call a representation (or a number system) complete and ... -
Using Automata Theory to Solve Problems in Additive Number Theory
(University of Waterloo, 2018-04-30)Additive number theory is the study of the additive properties of integers. Perhaps the best-known theorem is Lagrange’s result that every natural number is the sum of four squares. We study numbers whose base-k representations ...