Statistical Verification of Probabilistic Properties with Unbounded Until

  • Håkan L. S. Younes
  • Edmund M. Clarke
  • Paolo Zuliani
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6527)


We consider statistical (sampling-based) solution methods for verifying probabilistic properties with unbounded until. Statistical solution methods for probabilistic verification use sample execution trajectories for a system to verify properties with some level of confidence. The main challenge with properties that are expressed using unbounded until is to ensure termination in the face of potentially infinite sample execution trajectories. We describe two alternative solution methods, each one with its own merits. The first method relies on reachability analysis, and is suitable primarily for large Markov chains where reachability analysis can be performed efficiently using symbolic data structures, but for which numerical probability computations are expensive. The second method employs a termination probability and weighted sampling. This method does not rely on any specific structure of the model, but error control is more challenging. We show how the choice of termination probability—when applied to Markov chains—is tied to the subdominant eigenvalue of the transition probability matrix, which relates it to iterative numerical solution techniques for the same problem.


Markov Chain Model Check Probabilistic Property Reachability Analysis Symbolic Model Check 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Håkan L. S. Younes
    • 1
  • Edmund M. Clarke
    • 2
  • Paolo Zuliani
    • 2
  1. 1.Google IncUSA
  2. 2.Computer Science DepartmentCarnegie Mellon UniversityUSA

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