Date of Award

2018

Document Type

Thesis

Degree Name

Bachelors

Department

Natural Sciences

First Advisor

Henckell, Karsten

Area of Concentration

Mathematics

Abstract

This thesis surveys topics in Formal Language Theory and Automata Theory. Our goal is to exposit concepts like Regular, Context-Free, and Tree-Adjoining languages, and their associated grammars and automata. This area of mathematics arose out of an interest to classify and describe families of artificial languages. Linguists also exploited these results to shed light on the structure of natural languages. In the course of this exposition we mainly explore several theorems colloquially known as the Pumping Lemmata, which mainly serve as tools to prove that certain languages are not members of a class of languages. Each pumping lemma asserts that if a language is classified as Regular, Context-Free, or Tree-Adjoining, then any word in the language of suffcient length may be "pumped" (i.e. a number of substrings of the word may be either deleted or replaced by powers). Usually the pumping lemmata are used in the contrapositive form to assert that a language does not belong to a class because its strings cannot be pumped. In the end, we apply this to Mandarin Chinese to show that it may not be a Tree-Adjoining language provided that certain assumptions about what structures are grammatical in Chinese are correct.

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