Synthesis of Finite-state and Definable Winning Strategies
نویسنده
چکیده
Church’s Problem asks for the construction of a procedure which, given a logical specification φ on sequence pairs, realizes for any input sequence I an output sequenceO such that (I,O) satisfies φ. McNaughton reduced Church’s Problem to a problem about two-player ω-games. Büchi and Landweber gave a solution for Monadic Second-Order Logic of Order (MLO) specifications in terms of finite-state strategies. We consider two natural generalizations of the Church problem to countable ordinals: the first deals with finite-state strategies; the second deals with MLO-definable strategies. We investigate games of arbitrary countable length and prove the computability of these generalizations of Church’s problem.
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