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In formal language theory, the Büchi-Elgot-Trakhtenbrot theorem states that a language is regular if and only if it can be defined in monadic second-order logic (MSO): for every MSO formula, we can find a finite-state automaton (FSA) defining the same language, and for every FSA, we can find an MSO formula defining the same language. The theorem is due to Julius Richard Büchi, , and Boris Trakhtenbrot.
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