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Church Synthesis Problem with Parameters

  • Conference paper
Computer Science Logic (CSL 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4207))

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Abstract

The following problem is known as the Church Synthesis problem:

  • Input: an \({\mathit{MLO}}\) formula ψ(X,Y).

  • Task: Check whether there is an operator Y = F(X) such that

    $$Nat \models \forall X \psi(X,F(X))$$

    and if so, construct this operator.

Büchi and Landweber proved that the Church synthesis problem is decidable; moreover, they proved that if there is an operator F which satisfies ([1]), then ([1]) can be satisfied by the operator defined by a finite state automaton. We investigate a parameterized version of the Church synthesis problem. In this version ψ might contain as a parameter a unary predicate P. We show that the Church synthesis problem for P is computable if and only if the monadic theory of \(\langle{\mathit{Nat},<,P}\rangle\) is decidable. We also show that the Büchi-Landweber theorem can be extended only to ultimately periodic parameters.

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Author information

Authors and Affiliations

  1. Dept. of CS, Tel Aviv Univ.,  

    Alexander Rabinovich

Authors
  1. Alexander Rabinovich
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Editor information

Editors and Affiliations

  1. Research Group on Mathematical Linguistics, Rovira i Virgili University, Tarragona, Spain

    Zoltán Ésik

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Rabinovich, A. (2006). Church Synthesis Problem with Parameters. In: Ésik, Z. (eds) Computer Science Logic. CSL 2006. Lecture Notes in Computer Science, vol 4207. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11874683_36

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  • DOI: https://doi.org/10.1007/11874683_36

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-45458-8

  • Online ISBN: 978-3-540-45459-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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