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Permissive strategies: from parity games to safety games

Published online by Cambridge University Press:  15 December 2002

Julien Bernet ,
David Janin  and
Igor Walukiewicz
Julien Bernet
Affiliation:
LaBRI – CNRS – Université de Bordeaux I, 351 cours de la Libération, 33405 Talence Cedex, France; bernet@labri.fr. janinligw@labri.fr.
David Janin
Affiliation:
LaBRI – CNRS – Université de Bordeaux I, 351 cours de la Libération, 33405 Talence Cedex, France; bernet@labri.fr. janinligw@labri.fr.
Igor Walukiewicz
Affiliation:
LaBRI – CNRS – Université de Bordeaux I, 351 cours de la Libération, 33405 Talence Cedex, France; bernet@labri.fr. janinligw@labri.fr.
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Abstract

It is proposed to compare strategies in a parity game by comparing the sets of behaviours they allow. For such a game, there may be no winning strategy that encompasses all the behaviours of all winning strategies. It is shown, however, that there always exists a permissive strategy that encompasses all the behaviours of all memoryless strategies. An algorithm for finding such a permissive strategy is presented. Its complexity matches currently known upper bounds for the simpler problem of finding the set of winning positions in a parity game. The algorithm can be seen as a reduction of a parity to a safety game and computation of the set of winning positions in the resulting game.

Keywords

Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 36 , Issue 3 , July 2002 , pp. 261 - 275
Copyright
© EDP Sciences, 2002

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