TY - GEN

T1 - Synthesis of finite-state and definable winning strategies

AU - Rabinovich, Alexander

PY - 2009

Y1 - 2009

N2 - 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 sequence O 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.

AB - 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 sequence O 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.

UR - http://www.scopus.com/inward/record.url?scp=84880247609&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.FSTTCS.2009.2332

DO - 10.4230/LIPIcs.FSTTCS.2009.2332

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AN - SCOPUS:84880247609

SN - 9783939897132

T3 - Leibniz International Proceedings in Informatics, LIPIcs

SP - 359

EP - 370

BT - Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2009 - 29th Annual Conference, Proceedings

T2 - 29th International Conference on the Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2009

Y2 - 15 December 2009 through 17 December 2009

ER -