Hybrid Acceleration Using Real Vector Automata

  • Bernard Boigelot
  • Frédéric Herbreteau
  • Sébastien Jodogne
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2725)


This paper addresses the problem of computing an exact and effective representation of the set of reachable configurations of a linear hybrid automaton. Our solution is based on accelerating the state-space exploration by computing symbolically the repeated effect of control cycles. The computed sets of configurations are represented by Real Vector Automata (RVA), the expressive power of which is beyond that of the first-order additive theory of reals and integers. This approach makes it possible to compute in finite time sets of configurations that cannot be expressed as finite unions of convex sets. The main technical contributions of the paper consist in a powerful sufficient criterion for checking whether a hybrid transformation (i.e., with both discrete and continuous features) can be accelerated, as well as an algorithm for applying such an accelerated transformation on RVA. Our results have been implemented and successfully applied to several case studies, including the well-known leaking gas burner, and a simple communication protocol with timers.


Hybrid Automaton Region Graph Acceleration Method Reachability Problem Linear Hybrid 
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.


  1. [AAB00]
    Annichini, A., Asarin, E., Bouajjani, A.: Symbolic Techniques for Parametric Reasoning about Counters and Clock Systems. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 419–434. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  2. [ACH+95]
    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(1), 3–34 (1995)MATHCrossRefMathSciNetGoogle Scholar
  3. [AD94]
    Alur, R., Dill, D.L.: A theory of timed automata. Theoretical Computer Science 126(2), 183–235 (1994)MATHCrossRefMathSciNetGoogle Scholar
  4. [AHH93]
    Alur, R., Henzinger, T.A., Ho, P.-H.: Automatic symbolic verification of embedded systems. In: Proc. 14th annual IEEE Real-Time Systems Symposium, pp. 2–11 (1993)Google Scholar
  5. [BBR97]
    Boigelot, B., Bronne, L., Rassart, S.: An improved reachability analysis method for strongly linear hybrid systems. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 167–177. Springer, Heidelberg (1997)Google Scholar
  6. [BG96]
    Boigelot, B., Godefroid, P.: Symbolic verification of communication protocols with infinite state spaces using QDDs. In: Alur, R., Henzinger, T.A. (eds.) CAV 1996. LNCS, vol. 1102, pp. 1–12. Springer, Heidelberg (1996)Google Scholar
  7. [BH97]
    Bouajjani, A., Habermehl, P.: Symbolic reachability analysis of FIFO channel systems with nonregular sets of configurations. In: Degano, P., Gorrieri, R., Marchetti-Spaccamela, A. (eds.) ICALP 1997. LNCS, vol. 1256, pp. 560–570. Springer, Heidelberg (1997)Google Scholar
  8. [BJW01]
    Boigelot, B., Jodogne, S., Wolper, P.: On the use of weak automata for deciding linear arithmetic with integer and real variables. In: Goré, R.P., Leitsch, A., Nipkow, T. (eds.) IJCAR 2001. LNCS (LNAI), vol. 2083, pp. 611–625. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  9. [Boi99]
    Boigelot, B.: Symbolic Methods for Exploring Infinite State Spaces. Collection des publications de la Faculté des Sciences Appliquées de l’Université de Liège, Liège, Belgium (1999)Google Scholar
  10. [Bou03]
    Bouyer, P.: Untameable timed automata! In: Alt, H., Habib, M. (eds.) STACS 2003. LNCS, vol. 2607, pp. 620–631. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  11. [BRW98]
    Boigelot, B., Rassart, S., Wolper, P.: On the expressiveness of real and integer arithmetic automata. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 152–163. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  12. [BSW69]
    Bartlett, K.A., Scantlebury, R.A., Wilkinson, P.T.: A note on reliable full-duplex transmission over half-duplex links. Communications of the ACM 12(5), 260–261 (1969)CrossRefGoogle Scholar
  13. [BW94]
    Boigelot, B., Wolper, P.: Symbolic verification with periodic sets. In: Dill, D.L. (ed.) CAV 1994. LNCS, vol. 818, pp. 55–67. Springer, Heidelberg (1994)Google Scholar
  14. [CHR91]
    Chaochen, Z., Hoare, C.A.R., Ravn, A.P.: A calculus of durations. Information Processing Letters 40, 269–276 (1991)MATHCrossRefMathSciNetGoogle Scholar
  15. [CJ99]
    Comon, H., Jurski, Y.: Timed automata and the theory of real numbers. In: Baeten, J.C.M., Mauw, S. (eds.) CONCUR 1999. LNCS, vol. 1664, pp. 242–257. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  16. [Dil89]
    Dill, D.L.: Timing assumptions and verification of finite-state concurrent systems. In: Sifakis, J. (ed.) CAV 1989. LNCS, vol. 407, pp. 197–212. Springer, Heidelberg (1990)Google Scholar
  17. [Hen96]
    Henzinger, T.A.: The theory of hybrid automata. In: Proc. of the 11th Annual IEEE Symposium on Logic in Computer Science, New Brunswick, New Jersey, July 27–30, pp. 278–292. IEEE Computer Society Press, Los Alamitos (1996)CrossRefGoogle Scholar
  18. [HH94]
    Henzinger, T.A., Ho, P.-H.: Model checking strategies for linear hybrid systems. In: Proc. of Workshop on Formalisms for Representing and Reasoning about Time (May 1994)Google Scholar
  19. [HKPV98]
    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)MATHCrossRefMathSciNetGoogle Scholar
  20. [HL02]
    Hendriks, M., Larsen, K.G.: Exact acceleration of real-time model checking. Electronic Notes in Theoretical Computer Science 65(6) (April 2002)Google Scholar
  21. [HPR94]
    Halbwachs, N., Proy, Y.-E., Raymond, P.: Verification of linear hybrid systems by means of convex approximations. In: Dill, D.L. (ed.) CAV 1994. LNCS, vol. 818, pp. 223–237. Springer, Heidelberg (1994)Google Scholar
  22. [LASH]
    The Liège Automata-based Symbolic Handler (LASH). Available at,
  23. [Löd01]
    Löding, C.: Efficient minimization of deterministic weak ω−automata. Information Processing Letters 79(3), 105–109 (2001)MATHCrossRefMathSciNetGoogle Scholar
  24. [PLY99]
    Pappas, G.J., Lafferriere, G., Yovine, S.: A new class of decidable hybrid systems. In: Vaandrager, F.W., van Schuppen, J.H. (eds.) HSCC 1999. LNCS, vol. 1569, pp. 137–151. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  25. [WB95]
    Wolper, P., Boigelot, B.: An automata-theoretic approach to Presburger arithmetic constraints. In: Mycroft, A. (ed.) SAS 1995. LNCS, vol. 983, pp. 21–32. Springer, Heidelberg (1995)Google Scholar
  26. [Wei99]
    Weispfenning, V.: Mixed real-integer linear quantifier elimination. In: Proc. Of the 1999 International Symposium on Symbolic and Algebraic Computation (ISSAC), New York, pp. 129–136. ACM Press, New York (1999)CrossRefGoogle Scholar
  27. [Wey50]
    Weyl, H.: The elementary theory of convex polyhedra. Annals of Math. Study 24 (1950)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Bernard Boigelot
    • 1
  • Frédéric Herbreteau
    • 1
  • Sébastien Jodogne
    • 1
  1. 1.Institut Montefiore, B28Université de LiègeLiègeBelgium

Personalised recommendations