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Mu-depth 3 is more than 2: a game-theoretic proof

Published online by Cambridge University Press:  30 March 2001

LaBRI, Université Bordeaux I, 351, Cours de la Libération, F-33405 Talence cedex, France. Email: Dip. Mat. Appl. ‘U.Dini’, Università di Pisa, Via Bonanno 25B, 56100 Pisa, Italia.


We consider the propositional modal mu-calculus, a logic proposed by Kozen in 1983. In this logic two operators μ and v are present, which express the least and greatest fixpoints of monotone operators on sets. Bradfield in 1998 proved for any n the existence of a mu-calculus formula that requires n alternations of μ and v. In this paper we consider the particular case n = 3 and we exhibit a new formula requiring 3 alternations. Our proof is independent of the technique of Bradfield, and is based on a new kind of game on infinite trees.

Research Article
2001 Cambridge University Press

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