Abstract
1. THE PROBLEM Algebraic characterization of regular languages is one of the difficult parts in Automata Theory course. Typically, this part covers two topics. One is Nerod theorem: it provides an algebraic criterion for regularity of a language; for regular language it also provides a basis for understanding the structure of the minimal DFA that accepts it. Another topic is minimization of finite automata. Both topics are based on consideration of a variety of equivalences (general equivalence relation on words, rightinvariant equivalence, equivalence L R induced by a given language L, equivalence and k-equivalence of states, equivalence of automata). Moreover, relations between different equivalences (such as equality and refinement) are also employed. Being rather abstract, these concepts and techniques cause numerous difficulties and misconceptions that lead students to severe errors in problem solutions.
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