Fixed Point Iteration for Computing the Time Elapse Operator

  • Sriram Sankaranarayanan
  • Henny B. Sipma
  • Zohar Manna
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3927)


We investigate techniques for automatically generating symbolic approximations to the time solution of a system of differential equations. This is an important primitive operation for the safety analysis of continuous and hybrid systems. In this paper we design a time elapse operator that computes a symbolic over-approximation of time solutions to a continuous system starting from a given initial region. Our approach is iterative over the cone of functions (drawn from a suitable universe) that are non negative over the initial region. At each stage, we iteratively remove functions from the cone whose Lie derivatives do not lie inside the current iterate. If the iteration converges, the set of states defined by the final iterate is shown to contain all the time successors of the initial region. The convergence of the iteration can be forced using abstract interpretation operations such as widening and narrowing.

We instantiate our technique to linear hybrid systems with piecewise-affine dynamics to compute polyhedral approximations to the time successors. Using our prototype implementation TimePass, we demonstrate the performance of our technique on benchmark examples.


Hybrid System Continuous System Invariant Region Initial Region Reachable State 
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 2006

Authors and Affiliations

  • Sriram Sankaranarayanan
    • 1
    • 2
  • Henny B. Sipma
    • 2
  • Zohar Manna
    • 2
  1. 1.NEC Laboratories AmericaPrincetonUSA
  2. 2.Computer Science DepartmentStanford UniversityUSA

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