Model checking for a probabilistic branching time logic with fairness

  • Authors:

  • Christel Baier;Marta Kwiatkowska

  • Affiliations:

  • Fakultät für Mathematik & Informatik, Universitäät Mannheim, D-68131 Mannheim, Germany;School of Computer Science, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK

  • Venue:
  • Distributed Computing
  • Year:
  • 1998

Quantified Score

Hi-index 0.00

Visualization

Abstract

We consider concurrent probabilistic systems, based on probabilistic automata of Segala & Lynch [55], which allow non-deterministic choice between probability distributions. These systems can be decomposed into a collection of "computation trees" which arise by resolving the non-deterministic, but not probabilistic, choices. The presence of non-determinism means that certain liveness properties cannot be established unless fairness is assumed. We introduce a probabilistic branching time logic PBTL, based on the logic TPCTL of Hansson [30] and the logic PCTL of [55], resp. pCTL of [14]. The formulas of the logic express properties such as "every request is eventually granted with probability at least p". We give three interpretations for PBTL on concurrent probabilistic processes: the first is standard, while in the remaining two interpretations the branching time quantifiers are taken to range over a certain kind of fair computation trees. We then present a model checking algorithm for verifying whether a concurrent probabilistic process satisfies a PBTL formula assuming fairness constraints. We also propose adaptations of existing model checking algorithms for pCTL* [4, 14] to obtain procedures for PBTL* under fairness constraints. The techniques developed in this paper have applications in automatic verification of randomized distributed systems.