The (Nested) Word Problem: Formal Languages, Group Theory, and Languages of Nested Words

Abstract

<p>This thesis concerns itself with drawing out some interesting connections between the fields of group theory and formal language theory. Given a group with a finite set of generators, it is natural to consider the set of generators and their inverses as an alphabet. We can then consider formal languages such that every group element has at least one representative in the language. We examine what the structure of the language can tell us about group theoretic properties, focusing on the word problem, automatic structures on groups, and generalizations of automatic structures. Finally we prove new results concerning applications of languages of nested words for studying the word problem.</p>