Linear Parametric Model Checking of Timed Automata

  • Thomas Hune
  • Judi Romijn
  • Mariëelle Stoelinga
  • Frits Vaandrager
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2031)


We present an extension of the model checker Uppaal capable of synthesize linear parameter constraints for the correctness of parametric timed automata. The symbolic representation of the (parametric) state-space is shown to be correct. A second contribution of this paper is the identification of a subclass of parametric timed automata (L/U automata), for which the emptiness problem is decidable, contrary to the full class where it is know to be undecidable. Also we present a number of lemmas enabling the verification effort to be reduced for L/U automata in some cases. We illustrate our approach by deriving linear parameter constraints for a number of well-known case studies from the literature (exhibiting a flaw in a published paper).


  1. 1.
    R. Alur and D.L. Dill. A theory of timed automata. Theoretical Computer Science, 126:183–235, 1994.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    R. Alur, T.A. Henzinger, and M.Y. Vardi. Parametric real-time reasoning. In Proc. 25th Annual Symp. on Theory of Computing, pages 592–601. ACM Press, 1993.Google Scholar
  3. 3.
    A. Annichini, E. Asarin, and A. Bouajjani. Symbolic techniques for parametric reasoning about counter and clock systems. In Proc. 12th Int. Conference on Computer Aided Verification, LNCS 1855, pages 419–434. Springer-Verlag, 2000.CrossRefGoogle Scholar
  4. 4.
    G. Bandini, R. Lutje Spelberg, and H. Toetenel. Parametric verification of the IEEE 1394a root contention protocol using LPMC., July 2000. Submitted.
  5. 5.
    M. Bozga, C. Daws, O. Maler, A. Olivero, S. Tripakis, and S. Yovine. Kronos: A Model-Checking Tool for Real-Time Systems. In Proc. 10th Int. Conference on Computer Aided Verification, LNCS 1427, pages 546–550. Springer-Verlag, June/July 1998.CrossRefGoogle Scholar
  6. 6.
    T.H. Cormen, C.E. Leiserson, and R.L. Rivest. Introduction to Algorithms. McGraw-Hill, Inc., 1991.Google Scholar
  7. 7.
    P.R. D’Argenio, J.-P. Katoen, T.C. Ruys, and J. Tretmans. The bounded retransmission protocol must be on time! In Proc. Third Workshop on Tools and Algorithms for the Construction and Analysis of Systems, LNCS 1217, pages 416–431. Springer-Verlag, April 1997.CrossRefGoogle Scholar
  8. 8.
    D. Dill. Timing assumptions and verification of finite-state concurrent systems. In Proc. Int. Workshop on Automatic Verification Methods for Finite State Systems, LNCS 407, pages 197–212. Springer-Verlag, 1990.Google Scholar
  9. 9.
    T. A. Henzinger, P.-H. Ho, and H. Wong-Toi. HyTech: A Model Checker for Hybrid Systems. In Proc. 9th Int. Conference on Computer Aided Verification, LNCS 1254, pages 460–463. Springer-Verlag, 1997.Google Scholar
  10. 10.
    T.S. Hune, J.M.T. Romijn, M.I.A. Stoelinga, and F.W. Vaandrager. Linear parametric model checking of timed automata. Report CSI-R0102, CSI, University of Nijmegen, January 2001.Google Scholar
  11. 11.
    K. G. Larsen, P. Pettersson, and W. Yi. Uppaal in a Nutshell. Int. Journal on Software Tools for Technology Transfer, 1(1–2):134–152, October 1997.MATHCrossRefGoogle Scholar
  12. 12.
    R.F. Lutje Spelberg, W.J. Toetenel, and M. Ammerlaan. Partition refinement in real-time model checking. In Proc. FTRTFT’98, LNCS 1486, pages 143–157. Springer-Verlag, 1998.Google Scholar
  13. 13.
    D.P.L. Simons and M.I.A. Stoelinga. Mechanical verification of the IEEE 1394a root contention protocol using Uppaal2k. Technical Report CSI-R0009, CSI, University of Nijmegen, May 2000. Conditionally accepted for STTT.Google Scholar
  14. 14.
    M.I.A. Stoelinga and F.W. Vaandrager. Root contention in IEEE 1394. In Proc. 5th Int. AMAST Workshop on Formal Methods for Real-Time and Probabilistic Systems, LNCS 1601, pages 53–74. Springer-Verlag, 1999.CrossRefGoogle Scholar
  15. 15.
    S. Yovine. Model checking timed automata. In Lectures on Embedded Systems, LNCS 1494, pages 114–152. Springer-Verlag, October 1998.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Thomas Hune
    • 1
  • Judi Romijn
    • 2
  • Mariëelle Stoelinga
    • 2
  • Frits Vaandrager
    • 2
  1. 1.BRICSUniversity of ÅrhusDenmark
  2. 2.Computing Science InstituteUniversity of NijmegenNijmegen

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