In the diploma thesis, we deal with the formal language theory, where we discuss languages and operations on them. We define finite automata, learn their properties and address their relationship to words and languages. Through finite automata we define recognizable languages and connect them to the special class of languages called rational languages. In the work, we formulate Kleene’s theorem and give its proof. We introduce linear equations and systems of linear equations defined on languages. We determine conditions under which an equation or a system of equations has a unique solution. Arden's lemma and its proof are important in this result. We provide the algorithm that returns the corresponding rational language to a given finite automaton.
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