Synthesis of Finite-state and Definable Winning Strategies

Alexander Rabinovich, Marc Herbstritt
2009 Foundations of Software Technology and Theoretical Computer Science  
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
more » ... irst 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.
doi:10.4230/lipics.fsttcs.2009.2332 dblp:conf/fsttcs/Rabinovich09 fatcat:awc7tm6ulrgqzk7p3zrq4vhx5y