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Logical Refinements of Church’s Problem

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Book cover Computer Science Logic (CSL 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4646))

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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 \({\cal L}\) such that Church’s Problem with respect to \({\cal L}\) has also a solution in \({\cal L}\), and we discuss some perspectives of this approach.

This paper was written during a visit of the first author in Aachen in February 2007, funded by the European Science Foundation ESF in the Research Networking Programme AutoMathA (Automata: From Mathematics to Applications).

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Authors and Affiliations

  1. Tel Aviv University, Department of Computer Science,  

    Alexander Rabinovich

  2. RWTH Aachen, Lehrstuhl Informatik 7, 52056 Aachen, Germany

    Wolfgang Thomas

Authors
  1. Alexander Rabinovich
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  2. Wolfgang Thomas
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Jacques Duparc Thomas A. Henzinger

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© 2007 Springer-Verlag Berlin Heidelberg

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Rabinovich, A., Thomas, W. (2007). Logical Refinements of Church’s Problem. In: Duparc, J., Henzinger, T.A. (eds) Computer Science Logic. CSL 2007. Lecture Notes in Computer Science, vol 4646. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74915-8_9

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  • DOI: https://doi.org/10.1007/978-3-540-74915-8_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74914-1

  • Online ISBN: 978-3-540-74915-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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