Probabilistic Hybrid Systems Verification via SMT and Monte Carlo Techniques

  • Fedor Shmarov
  • Paolo Zuliani
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10028)


We develop numerically rigorous Monte Carlo approaches for computing probabilistic reachability in hybrid systems subject to random and nondeterministic parameters. Instead of standard simulation we use \(\delta \)-complete SMT procedures, which enable formal reasoning for nonlinear systems up to a user-definable numeric precision. Monte Carlo approaches for probability estimation assume that sampling is possible for the real system at hand. However, when using \(\delta \)-complete simulation one instead samples from an overapproximation of the real random variable. In this paper, we introduce a Monte Carlo-SMT approach for computing probabilistic reachability confidence intervals that are both statistically and numerically rigorous. We apply our technique to hybrid systems involving nonlinear differential equations.


Hybrid System Hybrid Automaton Real Random Variable Statistical Model Check Compute Confidence Interval 
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.



F.S. was supported by award N00014-13-1-0090 of the US Office of Naval Research; P.Z. was supported by EPSRC grant EP/N031962/1.


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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.School of Computing ScienceNewcastle UniversityNewcastle upon TyneUK

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