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VOLUME 3, ISSUE 4, PAPER 9
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The Church Synthesis Problem with Parameters
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©Alexander Rabinovich, Tel Aviv University
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Abstract
For a two-variable formula ψ(X,Y) of Monadic Logic of Order (MLO)
the Church Synthesis Problem concerns the existence and construction of an
operator Y=F(X) such that ψ(X,F(X)) is universally valid over
Nat.
Büchi and Landweber proved that the Church synthesis problem is
decidable; moreover, they showed that if there is an operator F that
solves the Church Synthesis Problem, then it can also be solved by an operator
defined by a finite state automaton or equivalently by an MLO formula. 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 is decidable. We prove that the
Büchi-Landweber theorem can be extended only to ultimately periodic
parameters. However, the MLO-definability part of the Büchi-Landweber
theorem holds for the parameterized version of the Church synthesis problem.
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Publication date: November 14, 2007
Full Text: PDF | PostScript
DOI: 10.2168/LMCS-3(4:9)2007
Hit Counts: 982 |
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