Mio, Matteo - On the equivalence of game and denotational semantics for the probabilistic mu-calculus

lmcs:787 - Logical Methods in Computer Science, June 1, 2012, Volume 8, Issue 2
On the equivalence of game and denotational semantics for the probabilistic mu-calculus

Authors: Mio, Matteo

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.


Source : oai:arXiv.org:1205.0126
DOI : 10.2168/LMCS-8(2:7)2012
Volume: Volume 8, Issue 2
Published on: June 1, 2012
Submitted on: March 21, 2012
Keywords: Computer Science - Logic in Computer Science,D.2.4, F.3.0, F.4.1


Share

Consultation statistics

This page has been seen 57 times.
This article's PDF has been downloaded 17 times.