Symbolic Model Checking of Hybrid Systems Using Template Polyhedra

  • Sriram Sankaranarayanan
  • Thao Dang
  • Franjo Ivančić
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4963)


We propose techniques for the verification of hybrid systems using template polyhedra, i.e., polyhedra whose inequalities have fixed expressions but with varying constant terms. Given a hybrid system description and a set of template linear expressions as inputs, our technique constructs over-approximations of the reachable states using template polyhedra. Therefore, operations used in symbolic model checking such as intersection, union and post-condition across discrete transitions over template polyhedra can be computed efficiently using template polyhedra without requiring expensive vertex enumeration.

Additionally, the verification of hybrid systems requires techniques to handle the continuous dynamics inside discrete modes. We propose a new flowpipe construction algorithm using template polyhedra. Our technique uses higher-order Taylor series expansion to approximate the time trajectories. The terms occurring in the Taylor series expansion are bounded using repeated optimization queries. The location invariant is used to enclose the remainder term of the Taylor series, and thus truncate the expansion. Finally, we have implemented our technique as a part of the tool TimePass for the analysis of affine hybrid automata.


Hybrid System Taylor Series Expansion Remainder Term Hybrid Automaton Abstract Domain 
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 2008

Authors and Affiliations

  • Sriram Sankaranarayanan
    • 1
  • Thao Dang
    • 2
  • Franjo Ivančić
    • 1
  1. 1.NEC Laboratories AmericaPrincetonUSA
  2. 2.Verimag, GrenobleFrance

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