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Decidable Extensions of Church’s Problem

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Computer Science Logic (CSL 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5771))

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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.

Büchi 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.

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Author information

Authors and Affiliations

  1. The Blavatnik School of Computer Science, Tel Aviv University, Israel

    Alexander Rabinovich

Authors
  1. Alexander Rabinovich
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Editor information

Editors and Affiliations

  1. Mathematische Grundlagen der Informatik, RWTH Aachen, 52056, Aachen, Germany

    Erich Grädel

  2. CENTRIA and Departamento de Matemática, Universidade Nova de Lisboa, 2829-516, Caparica, Portugal

    Reinhard Kahle

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Rabinovich, A. (2009). Decidable Extensions of Church’s Problem. In: Grädel, E., Kahle, R. (eds) Computer Science Logic. CSL 2009. Lecture Notes in Computer Science, vol 5771. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04027-6_31

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  • DOI: https://doi.org/10.1007/978-3-642-04027-6_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04026-9

  • Online ISBN: 978-3-642-04027-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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