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URN: urn:nbn:de:0030-drops-23320
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### 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},