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International Workshop on Computer Science Logic

CSL 2003: Computer Science Logic pp 183–196Cite as

Positive Games and Persistent Strategies

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2803))

Abstract

At CSL 2002, Jerzy Marcinkowsi and Tomasz Truderung presented the notions of positive games and persistent strategies [8]. A strategy is persistent if, given any finite or infinite run played on a game graph, each time the player visits some vertex already encountered, this player repeats the decision made when visiting this vertex for the first time. Such strategies require memory, but once a choice is made, it is made for ever. So, persistent strategies are a weakening of memoryless strategies.

The same authors established a direct relation between positive games and the existence of persistent winning strategies. We give a description of such games by means of their topological complexity. In games played on finite graphs, positive games are unexpectedly simple. On the contrary, infinite game graphs, as well as infinite alphabets, yield positive sets involved in non determined games.

Last, we discuss positive Muller winning conditions. Although they do not help to discriminate between memoryless and LAR winning strategies, they bear a strong topological characterization.

The author sincerely thanks Erich Grädel for numerous remarks and corrections.

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Author information

Authors and Affiliations

  1. LuFG Mathematische Grundlagen der Informatik, RWTH-Aachen, D-52056, Aachen

    Jacques Duparc

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  1. Jacques Duparc
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Editor information

Editors and Affiliations

  1. Institute of Discrete Mathematics and Geometry, Technical University Vienna, Wiedner Hauptstrasse 8-10, A-1040, Wien, Austria

    Matthias Baaz

  2. Members of EACSL Jury for the Ackermann Award,  

    Johann A. Makowsky

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© 2003 Springer-Verlag Berlin Heidelberg

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Duparc, J. (2003). Positive Games and Persistent Strategies. In: Baaz, M., Makowsky, J.A. (eds) Computer Science Logic. CSL 2003. Lecture Notes in Computer Science, vol 2803. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45220-1_17

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  • DOI: https://doi.org/10.1007/978-3-540-45220-1_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40801-7

  • Online ISBN: 978-3-540-45220-1

  • eBook Packages: Springer Book Archive

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