Logical refinements of Church's problem

Authors:
Alexander Rabinovich;Wolfgang Thomas
Affiliations:
Tel Aviv University, Department of Computer Science;RWTH Aachen, Aachen, Germany
Venue:
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
Year:
2007

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Abstract

Church's Problem (1962) asks for the construction of a procedure which, given a logical specification ϕ on sequence pairs, realizes for any input sequence X an output sequence Y such that (X,Y) satisfies ϕ. Büchi and Landweber (1969) gave a solution for MSO specifications in terms of finite-state automata. We address the problem in a more general logical setting where not only the specification but also the solution is presented in a logical system. Extending the result of Büchi and Landweber, we present several logics L such that Church's Problem with respect to L has also a solution in L, and we discuss some perspectives of this approach.