License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license (CC BY-NC-ND 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CSL.2011.307
URN: urn:nbn:de:0030-drops-32390
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2011/3239/
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Jenkins, Mark ; Ouaknine, Joël ; Rabinovich, Alexander ; Worrell, James

The Church Synthesis Problem with Metric

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Abstract

Church's Problem asks for the construction of a procedure which, given a logical specification S(I,O) between input strings I and output strings O, determines whether there exists an operator F that implements the specification in the sense that S(I,F(I)) holds for all inputs I. Buechi and Landweber gave a procedure to solve Church's problem for MSO specifications and operators computable by finite-state automata.

We consider extensions of Church's problem in two orthogonal directions: (i) we address the problem in a more general logical setting, where not only the specifications but also the solutions are presented in a logical system; (ii) we consider not only the canonical discrete time domain of the natural numbers, but also the continuous domain of reals.

We show that for every fixed bounded length interval of the reals, Church's problem is decidable when specifications and implementations are described in the monadic second-order logics over the reals with order and the +1 function.

BibTeX - Entry

@InProceedings{jenkins_et_al:LIPIcs:2011:3239,
  author =	{Mark Jenkins and Jo{\"e}l Ouaknine and Alexander Rabinovich and James Worrell},
  title =	{{The Church Synthesis Problem with Metric}},
  booktitle =	{Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL},
  pages =	{307--321},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-32-3},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{12},
  editor =	{Marc Bezem},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2011/3239},
  URN =		{urn:nbn:de:0030-drops-32390},
  doi =		{10.4230/LIPIcs.CSL.2011.307},
  annote =	{Keywords: Church's Problem, monadic logic, games, uniformization}
}

Keywords: Church's Problem, monadic logic, games, uniformization
Collection: Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL
Issue Date: 2011
Date of publication: 31.08.2011

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