Synthesis of Finite-state and Definable Winning Strategies

Rabinovich, Alexander

doi:10.4230/LIPIcs.FSTTCS.2009.2332

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Synthesis of Finite-state and Definable Winning Strategies

Author Alexander Rabinovich

Part of: Volume: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2009)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: Conference: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS)
License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
Publication Date: 2009-12-14

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Document Identifiers

DOI: 10.4230/LIPIcs.FSTTCS.2009.2332
URN: urn:nbn:de:0030-drops-23320

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Keywords

Games of ordinal length
Church Synthesis Problem
Monadic Logic
Composition Method

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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.

Cite As Get BibTex

Alexander Rabinovich. Synthesis of Finite-state and Definable Winning Strategies. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 359-370, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009) https://doi.org/10.4230/LIPIcs.FSTTCS.2009.2332

Author Details

Alexander Rabinovich

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