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Automatic Rectangular Refinement of Affine Hybrid Systems

  • Laurent Doyen
  • Thomas A. Henzinger
  • Jean-François Raskin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3829)

Abstract

We show how to automatically construct and refine rectangular abstractions of systems of linear differential equations. From a hybrid automaton whose dynamics are given by a system of linear differential equations, our method computes automatically a sequence of rectangular hybrid automata that are increasingly precise overapproximations of the original hybrid automaton. We prove an optimality criterion for successive refinements. We also show that this method can take into account a safety property to be verified, refining only relevant parts of the state space. The practicability of the method is illustrated on a benchmark case study.

Keywords

Hybrid System Safety Property Hybrid Automaton Reachability Analysis Simulation Relation 
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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References

  1. 1.
    Alur, R., Courcoubetis, C., Halbwachs, N., Henzinger, T.A., Ho, P.-H., Nicollin, X., Olivero, A., Sifakis, J., Yovine, S.: The algorithmic analysis of hybrid systems. Theoretical Computer Science 138, 3–34 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Asarin, E., Dang, T., Maler, O., Bournez, O.: Approximate reachability analysis of piecewise-linear dynamical systems. In: Lynch, N.A., Krogh, B.H. (eds.) HSCC 2000. LNCS, vol. 1790, pp. 20–31. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  3. 3.
    Bagnara, R., Ricci, E., Zaffanella, E., Hill, P.M.: Possibly not closed convex polyhedra and the Parma Polyhedra Library. In: Hermenegildo, M.V., Puebla, G. (eds.) SAS 2002. LNCS, vol. 2477, pp. 213–229. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  4. 4.
    Clarke, E.M., Grumberg, O., Jha, S., Lu, Y., Veith, H.: Counterexample-guided abstraction refinement. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 154–169. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  5. 5.
    Fehnker, A., Ivancic, F.: Benchmarks for hybrid systems verification. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 326–341. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  6. 6.
    Fränzle, M.: Analysis of hybrid systems: An ounce of realism can save an infinity of states. In: Flum, J., Rodríguez-Artalejo, M. (eds.) CSL 1999. LNCS, vol. 1683, pp. 126–140. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  7. 7.
    Frehse, G.: Phaver: Algorithmic verification of hybrid systems past HYTECH. In: Morari, M., Thiele, L. (eds.) HSCC 2005. LNCS, vol. 3414, pp. 258–273. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  8. 8.
    Henzinger, T.A.: The theory of hybrid automata. In: Proceedings of the 11th Annual Symposium on Logic in Computer Science, pp. 278–292. IEEE Computer Society Press, Los Alamitos (1996)CrossRefGoogle Scholar
  9. 9.
    Henzinger, T.A., Ho, P.-H., Wong-Toi, H.: A user guide to HyTech. In: Brinksma, E., Steffen, B., Cleaveland, W.R., Larsen, K.G., Margaria, T. (eds.) TACAS 1995. LNCS, vol. 1019, pp. 41–71. Springer, Heidelberg (1995)Google Scholar
  10. 10.
    Henzinger, T.A., Ho, P.-H., Wong-Toi, H.: Algorithmic analysis of nonlinear hybrid systems. IEEE Transactions on Automatic Control 43, 540–554 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Henzinger, T.A., Kopke, P.W., Puri, A., Varaiya, P.: What’s decidable about hybrid automata? Journal of Computer and System Sciences 57, 94–124 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Milner, R.: A Calculus of Communication Systems. LNCS, vol. 92. Springer, Heidelberg (1980)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Laurent Doyen
    • 1
  • Thomas A. Henzinger
    • 2
    • 3
  • Jean-François Raskin
    • 1
  1. 1.Université Libre de Bruxelles (ULB) BrusselsBelgium
  2. 2.École Polytechnique Fédérale de Lausanne (EPFL)LausanneSwitzerland
  3. 3.University of California (UC) BerkeleyU.S.A.

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