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Monadic Second Order Logic and Automata on Infinite Words : Büchi ’ s Theorem

Büchi’s theorem establishes the equivalence of the satisfiability relation for monadic second-order logic, and the acceptance relation for Büchi automata. The development of the theories of monadic second-order logic and Büchi automata follows Thomas’s survey[6] closely, in that all of the concepts and results found in this report are also in [6]. However, because the scope of Thomas’s survey is much greater, he develops the theories in a more general (and more complicated) way than is necessary to understand Büchi’s theorem, and he only sketches the proof of Büchi’s theorem, which is given in detail here.