Skip to Main content Skip to Navigation
Journal articles

On the equivalence of game and denotational semantics for the probabilistic μ -calculus

Matteo Mio 1, 2
1 COMETE - Concurrency, Mobility and Transactions
Inria Saclay - Ile de France, LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
Abstract : The probabilistic (or quantitative) modal mu-calculus is a fixed-point logic de- signed for expressing properties of probabilistic labeled transition systems (PLTS). Two semantics have been studied for this logic, both assigning to every process state a value in the interval [0,1] representing the probability that the property expressed by the formula holds at the state. One semantics is denotational and the other is a game semantics, specified in terms of two-player stochastic games. The two semantics have been proved to coincide on all finite PLTS's, but the equivalence of the two semantics on arbitrary models has been open in literature. In this paper we prove that the equivalence indeed holds for arbitrary infinite models, and thus our result strengthens the fruitful connection between denotational and game semantics. Our proof adapts the unraveling or unfolding method, a general proof technique for proving result of parity games by induction on their complexity.
Document type :
Journal articles
Complete list of metadata
Contributor : Matteo Mio <>
Submitted on : Monday, December 10, 2012 - 6:57:20 PM
Last modification on : Monday, December 14, 2020 - 3:33:07 PM

Links full text


  • HAL Id : hal-00763454, version 1
  • ARXIV : 1205.0126



Matteo Mio. On the equivalence of game and denotational semantics for the probabilistic μ -calculus. Logical Methods in Computer Science, Logical Methods in Computer Science Association, 2012, 8 (2), pp.1-21. ⟨hal-00763454⟩



Record views