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DOI: 10.4230/LIPIcs.FSTTCS.2009.2332
URN: urn:nbn:de:0030-drops-23320
URL: http://drops.dagstuhl.de/opus/volltexte/2009/2332/
Rabinovich, Alexander

Synthesis of Finite-state and Definable Winning Strategies

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Abstract

Church's Problem asks for the construction of a procedure which, given a logical specification $\varphi$ on sequence pairs, realizes for any input sequence $I$ an output sequence $O$ such that $(I,O)$ satisfies $\varphi$. McNaughton reduced Church's Problem to a problem about two-player$\omega$-games. B\"uchi and Landweber gave a solution for Monadic Second-Order Logic of Order ($\MLO$) specifications in terms of finite-state strategies. We consider two natural generalizations of the Church problem to countable ordinals: the first deals with finite-state strategies; the second deals with $\MLO$-definable strategies. We investigate games of arbitrary countable length and prove the computability of these generalizations of Church's problem.

BibTeX - Entry

@InProceedings{rabinovich:LIPIcs:2009:2332,
  author =	{Alexander Rabinovich},
  title =	{Synthesis of Finite-state and Definable Winning Strategies},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2009)},
  pages =	{359--370},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-13-2},
  ISSN =	{1868-8969},
  year =	{2009},
  volume =	{4},
  editor =	{Ravi Kannan and K Narayan Kumar},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2009/2332},
  URN =		{urn:nbn:de:0030-drops-23320},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.FSTTCS.2009.2332},
  annote =	{Keywords: Games of ordinal length, Church Synthesis Problem, Monadic Logic, Composition Method}
}

Keywords: Games of ordinal length, Church Synthesis Problem, Monadic Logic, Composition Method
Seminar: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science
Issue date: 2009
Date of publication: 14.12.2009

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