Permissive strategies: from parity games to safety games

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.

• Type: Journal
• Year: 2002
• Where: ITA
• Authors: Julien Bernet, David Janin, Igor Walukiewicz
• Keywords: Behaviours, Communications, ITA 2002, Parity Game, Permissive Strategy