[KKNP08a] Mark Kattenbelt, Marta Kwiatkowska, Gethin Norman and David Parker. Game-Based Probabilistic Predicate Abstraction in PRISM. In Proc. 6th Workshop on Quantitative Aspects of Programming Languages (QAPL'08), volume 220 (3) of Electronic Notes in Theoretical Computer Science , pages 5-21 , Elsevier. March 2008. [ps.gz] [pdf] [bib] [Develops predicate abstraction techniques for PRISM, using SMT and game-based abstraction.]
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Notes: Proofs can be found in the technical report version of this paper [KKNP08b].
Abstract. Modelling and verification of systems such as communication, network and security protocols, which exhibit both probabilistic and non-deterministic behaviour, typically use Markov Decision Processes (MDPs). For large, complex systems, abstraction techniques are essential. This paper builds on a promising approach for abstraction of MDPs based on stochastic two-player games which provides distinct lower and upper bounds for minimum and maximum probabilistic reachability properties. Existing implementations work at the model level, limiting their scalability. In this paper, we develop language-level abstraction techniques that build game-based abstractions of MDPs directly from high-level descriptions in the PRISM modelling language, using predicate abstraction and SMT solvers. For efficiency, we develop a compositional framework for abstraction. We have applied our techniques to a range of case studies, successfully verifying models larger than was possible with existing implementations. We are also able to demonstrate the benefits of adopting a compositional approach.