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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSTTCS.2009.2332
URN: urn:nbn:de:0030-drops-23320
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2009/2332/
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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},
  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 =		{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
Collection: 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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