Advertisement

A Compositional Algorithm for Parallel Model Checking of Polygonal Hybrid Systems

  • Gordon Pace
  • Gerardo Schneider
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4281)

Abstract

The reachability problem as well as the computation of the phase portrait for the class of planar hybrid systems defined by constant differential inclusions (SPDI), has been shown to be decidable. The existing reachability algorithm is based on the exploitation of topological properties of the plane which are used to accelerate certain kind of cycles. The complexity of the algorithm makes the analysis of large systems generally unfeasible. In this paper we present a compositional parallel algorithm for reachability analysis of SPDIs. The parallelization is based on the qualitative information obtained from the phase portrait of an SPDI, in particular the controllability kernel.

Keywords

Phase Portrait Multivalued Function Feasible Path Hybrid Automaton Reachability Analysis 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [AD94]
    Alur, R., Dill, D.L.: A theory of timed automata. Theoretical Computer Science 126, 183–235 (1994)MATHCrossRefMathSciNetGoogle Scholar
  2. [APSY02]
    Asarin, E., Pace, G.J., Schneider, G., Yovine, S.: SPeeDI - A verification tool for polygonal hybrid systems. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 354–358. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  3. [AS02]
    Asarin, E., Schneider, G.: Widening the boundary between decidable and undecidable hybrid systems. In: Brim, L., Jančar, P., Křetínský, M., Kucera, A. (eds.) CONCUR 2002. LNCS, vol. 2421, pp. 193–208. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  4. [ASY01]
    Asarin, E., Schneider, G., Yovine, S.: On the decidability of the reachability problem for planar differential inclusions. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A.L. (eds.) HSCC 2001. LNCS, vol. 2034, pp. 89–104. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  5. [ASY02]
    Asarin, E., Schneider, G., Yovine, S.: Towards computing phase portraits of polygonal differential inclusions. In: Tomlin, C.J., Greenstreet, M.R. (eds.) HSCC 2002. LNCS, vol. 2289, p. 49. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  6. [FvDFH96]
    Foley, J.D., van Dam, A., Feiner, S.K., Hughes, J.F.: Computer graphics (2nd ed. in C): principles and practice. Addison-Wesley Longman Publishing Co., Inc., Boston (1996)Google Scholar
  7. [Hen79]
    Henle, M.: A combinatorial introduction to topology. Dover publications, Inc., Mineola (1979)MATHGoogle Scholar
  8. [HKPV95]
    Henzinger, T.A., Kopke, P.W., Puri, A., Varaiya, P.: What’s decidable about hybrid automata? In: STOC 1995, pp. 373–382. ACM Press, New York (1995)CrossRefGoogle Scholar
  9. [LPY01]
    Lafferriere, G., Pappas, G., Yovine, S.: Symbolic reachability computation of families of linear vector fields. Journal of Symbolic Computation 32(3), 231–253 (2001)MATHCrossRefMathSciNetGoogle Scholar
  10. [MP93]
    Maler, O., Pnueli, A.: Reachability analysis of planar multi-linear systems. In: Courcoubetis, C. (ed.) CAV 1993. LNCS, vol. 697, pp. 194–209. Springer, Heidelberg (1993)Google Scholar
  11. [PS03]
    Pace, G.J., Schneider, G.: Model checking polygonal differential inclusions using invariance kernels. In: Steffen, B., Levi, G. (eds.) VMCAI 2004. LNCS, vol. 2937, pp. 110–121. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  12. [PS06]
    Pace, G., Schneider, G.: Static analysis of SPDIs for state-space reduction. Technical Report 336, Department of Informatics, University of Oslo, PO Box 1080 Blindern, N-0316 Oslo, Norway (April 2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Gordon Pace
    • 1
  • Gerardo Schneider
    • 2
  1. 1.Dept. of Computer Science and AIUniversity of MaltaMsidaMalta
  2. 2.Dept. of InformaticsUniversity of OsloOsloNorway

Personalised recommendations