On the equivalence of game and denotational semantics for the probabilistic μ -calculus - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Logical Methods in Computer Science Year : 2012

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

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.

Dates and versions

hal-00763454 , version 1 (10-12-2012)

Identifiers

Cite

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

Altmetric

Share

Gmail Facebook X LinkedIn More