Uniform Sampling for Timed Automata with Application to Language Inclusion Measurement

  • Benoît Barbot
  • Nicolas BassetEmail author
  • Marc Beunardeau
  • Marta Kwiatkowska
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9826)


Monte Carlo model checking introduced by Smolka and Grosu is an approach to analyse non-probabilistic models using sampling and draw conclusions with a given confidence interval by applying statistical inference. Though not exhaustive, the method enables verification of complex models, even in cases where the underlying problem is undecidable. In this paper we develop Monte Carlo model checking techniques to evaluate quantitative properties of timed languages. Our approach is based on uniform random sampling of behaviours, as opposed to isotropic sampling that chooses the next step uniformly at random. The uniformity is defined with respect to volume measure of timed languages previously studied by Asarin, Basset and Degorre. We improve over their work by employing a zone graph abstraction instead of the region graph abstraction and incorporating uniform sampling within a zone-based Monte Carlo model checking framework. We implement our algorithms using tools PRISM, SageMath and COSMOS, and demonstrate their usefulness on statistical language inclusion measurement in terms of volume.


Probability Density Function Volume Function Uniform Sampling Hybrid Automaton Entry Zone 
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 International Publishing Switzerland 2016

Authors and Affiliations

  • Benoît Barbot
    • 1
  • Nicolas Basset
    • 1
    Email author
  • Marc Beunardeau
    • 2
    • 3
  • Marta Kwiatkowska
    • 1
  1. 1.Department of Computer ScienceUniversity of OxfordOxfordUK
  2. 2.Ingenico LabsParisFrance
  3. 3.École Normale SupérieureParisFrance

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