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PODC '90 Proceedings of the ninth annual ACM symposium on Principles of distributed computing
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QEST '06 Proceedings of the 3rd international conference on the Quantitative Evaluation of Systems
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CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
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CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
PRISM: a tool for automatic verification of probabilistic systems
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A game-based abstraction-refinement framework for Markov decision processes
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Theoretical Computer Science
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VMCAI'10 Proceedings of the 11th international conference on Verification, Model Checking, and Abstract Interpretation
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TACAS'10 Proceedings of the 16th international conference on Tools and Algorithms for the Construction and Analysis of Systems
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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.