Hierarchie regulárních jazyků

The main goal of this thesis is to provide an overview of main results in algebraic theory of regular languages. Every regular language is associated with finite semigroup or monoid. We introduce a notion of pseudovarieties of finite (ordered) semigroups and monoids, which are in one-to-one correspondence with (positive) varieties of regular languages. Regular languages can also be characterized by finite automata. We define C-variety of automata and prove the Eilenberg correspondence between complete lattice of C-varieties of automata and complete lattice of C-varieties of regular languages. We will also show some examples of different concatenation hierarchies and subhierarchies of regular languages as well as few C-varieties of automata and their associated C-varieties of languages.