  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.
