On the Use of Quasiorders in Formal Language Theory

TL;DR

This thesis introduces a novel quasiorder-based framework for addressing key problems in Formal Language Theory, including language inclusion and automata manipulation, leading to new algorithms and insights.

Contribution

It presents a generic framework using quasiorders that unifies and extends existing methods for language inclusion and automata construction, including new algorithms.

Findings

New quasiorder-based algorithms for language inclusion

Efficient regex search on compressed text using the framework

A novel perspective on residual automata construction

Abstract

In this thesis we use quasiorders on words to offer a new perspective on two well-studied problems from Formal Language Theory: deciding language inclusion and manipulating the finite automata representations of regular languages. First, we present a generic quasiorder-based framework that, when instantiated with different quasiorders, yields different algorithms (some of them new) for deciding language inclusion. We then instantiate this framework to devise an efficient algorithm for searching with regular expressions on grammar-compressed text. Finally, we define a framework of quasiorder-based automata constructions to offer a new perspective on residual automata.