Decidable Extensions of Church's Problem

Abstract. For a two-variable formula B(X,Y) of Monadic Logic of Order (MLO) the Church Synthesis Problem concerns the existence and construction of a finite-state operator Y=F(X) such that B(X,F(X)) is universally valid over Nat. B¨uchi and Landweber (1969) proved that the Church synthesis problem is decidable. We investigate a parameterized version of the Church synthesis problem. In this extended version a formula B and a finite-state operator F might contain as a parameter a unary predicate P. A large class of predicates P is exhibited such that the Church problem with the parameter P is decidable. Our proofs use Composition Method and game theoretical techniques.

• Type: Conference
• Year: 2009
• Where: CSL
• Authors: Alexander Rabinovich
• Keywords: Artificial Intelligence, Church Synthesis Problem, CSL 2009, Unary Predicate P, finite-state Operator