Task-system analysis using slope-parametric hybrid automata

  • Augusto Burgueño
  • Vlad Rusu
Workshop 20: Real-Time Systems and Constraints
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1300)


Slope-parametric hybrid automata (SPHA) are hybrid automata whose variables can have parametric slopes. SPHA are useful, in particular, for modeling task-control systems in which the task speeds can be adjusted for meeting some safety requirement. In this paper, we present an example of parametric analysis for a simple task system. We introduce a prototype verification tool that fully automates the analysis.


real-time systems hybrid automata parametric polyhedra 


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  1. ACH+95.
    R. Alur, C. Courcoubetis, N. Halbwachs, T. A. Henzinger, P-H. Ho, X. Nicollin, A. Olivero, J. Sifakis, and S. Yovine. The algorithmic analysis of hybrid systems. TCS, 138:3–34, 1995.Google Scholar
  2. AHH93.
    R. Alur, T. A. Henzinger, and P-H. Ho. Automatic symbolic verification of embedded systems. In Proc. IEEE RTSS'93, pages 2–11, 1993.Google Scholar
  3. AHV93.
    R. Alur, T. A. Henzinger, and M. Y. Vardi. Parametric real-time reasoning. In Proc. ACM STOC'93, pages 592–601, 1993.Google Scholar
  4. BBRR97.
    F. Boniol, A. Burgueño, O. Roux, and V. Rusu. Analysis of slope-parametric hybrid automata. In Proc. HART'97, volume 1201 of LNCS, pages 75–80, 1997.Google Scholar
  5. BGK+96.
    J. Bengtsson, D. Griffioen, K. Kristoffersen, K. G. Larsen, F. Larsson, P. Pettersson, and W. Yi. Verification of an audio protocol with bus collision using UPPAAL. In Proc. CA V'96, volume 1102 of LNCS, 1996.Google Scholar
  6. Bro81.
    R. A. Brooks. Symbolic reasoning among 3-D models and 2-D images. Art. Int., 17:285–348, 1981.Google Scholar
  7. CABN97.
    W. Chan, R. Anderson, P. Beame, and D. Notkin. Combining constraint solving and symbolic model checking for a class of systems with non-linear constraints. In Proc. CAV'97, 1997.Google Scholar
  8. CY91.
    C. Courcoubetis and M. Yannakakis. Minimum and maximun delay problems in real-time systems. In Proc. CAV'91, volume 575 of LNCS, pages 399–409, 1991.Google Scholar
  9. DY95.
    C. Daws and S. Yovine. Two examples of verification of multirate timed automata with Kronos. In Proc. IEEE RTSS'95, 1995.Google Scholar
  10. HH94.
    T. A. Henzinger and P.-H. Ho. HyTech: the Cornell HYbrid TECHnology tool. In Hybrid Systems II, volume 999 of LNCS, pages 265–294, 1994.Google Scholar
  11. HLM97.
    M. Heymann, F. Lin, and G. Meyer. Control synthesis for a class of hybrid systems subject to configuration-based constraints. In Proc. HART'97, volume 1201 of LNCS, pages 376–390, 1997.Google Scholar
  12. HNSY94.
    T. A. Henzinger, X. Nicollin, J. Sifakis, and S. Yovine. Symbolic model checking for real-time systems. Inf. and Comp., 111(2):193–244, 1994.Google Scholar
  13. KS97.
    D. Kapur and R. K. Shyamasundar. Synthesizing controllers for hybrid systems. In Proc. HART'97, volume 1201 of LNCS, pages 361–375, 1997.Google Scholar
  14. Sac87.
    E. Sacks. Hierarchical reasoning about inequalities. In Proc. AAAI'87, volume 2, pages 649–654, 1987.Google Scholar
  15. Wan96.
    F. Wang. Parametric timing analysis for real-time systems. Inf. and Comp., 130(2):131–150, 1996.Google Scholar
  16. Zie95.
    G. M. Ziegler. Lectures on Polytopes, volume 152 of Graduate Texts in Mathematics. Springer-Verlag, 1995. *** DIRECT SUPPORT *** A0008C42 00044Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Augusto Burgueño
    • 1
  • Vlad Rusu
    • 2
  1. 1.Département d'InformatiqueONERA-CERTToulouse Cedex 4France
  2. 2.IRCyN (UMR CNRS N. 6597, Ecole Centrale de Nantes, Université de Nantes)Nantes Cedex 3France

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