The Power of Hybrid Acceleration

  • Bernard Boigelot
  • Frédéric Herbreteau
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4144)


This paper addresses the problem of computing symbolically the set of reachable configurations of a linear hybrid automaton. A solution proposed in earlier work consists in exploring the reachable configurations using an acceleration operator for computing the iterated effect of selected control cycles. Unfortunately, this method imposes a periodicity requirement on the data transformations labeling these cycles, that is not always satisfied in practice. This happens in particular with the important subclass of timed automata, even though it is known that the paths of such automata have a periodic behavior.

The goal of this paper is to broaden substantially the applicability of hybrid acceleration. This is done by introducing powerful reduction rules, aimed at translating hybrid data transformations into equivalent ones that satisfy the periodicity criterion. In particular, we show that these rules always succeed in the case of timed automata. This makes it possible to compute an exact symbolic representation of the set of reachable configurations of a linear hybrid automaton, with a guarantee of termination over the subclass of timed automata. Compared to other known solutions to this problem, our method is simpler, and applicable to a much larger class of systems.


Reduction Rule Simple Loop Hybrid Automaton Time Automaton 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.


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  1. [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
  2. [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
  3. [BHJ03]
    Boigelot, B., Herbreteau, F., Jodogne, S.: Hybrid acceleration using real vector automata. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 193–205. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  4. [BJW05]
    Boigelot, B., Jodogne, S., Wolper, P.: An effective decision procedure for linear arithmetic with integer and real variables. ACM Transactions on Computational Logic (TOCL) 6(3), 614–633 (2005)CrossRefMathSciNetGoogle Scholar
  5. [BLFP03]
    Bardin, S., Leroux, J., Finkel, A., Petrucci, L.: FAST: Fast accelereation of symbolic transition systems. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 118–121. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  6. [BLR05]
    Bouyer, P., Laroussinie, F., Reynier, P.-A.: Diagonal constraints in timed automata: Forward analysis of timed systems. In: Pettersson, P., Yi, W. (eds.) FORMATS 2005. LNCS, vol. 3829, pp. 112–126. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  7. [Boi98]
    Boigelot, B.: Symbolic Methods for Exploring Infinite State Spaces. PhD thesis, Université de Liège (1998)Google Scholar
  8. [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
  9. [BY03]
    Bengtsson, J., Yi, W.: On clock difference constraints and termination in reachability analysis of timed automata. In: Dong, J.S., Woodcock, J. (eds.) ICFEM 2003. LNCS, vol. 2885, pp. 491–503. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  10. [CJ98]
    Comon, H., Jurski, Y.: Multiple counters automata, safety analysis and Presburger arithmetic. In: Y. Vardi, M. (ed.) CAV 1998. LNCS, vol. 1427, pp. 268–279. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  11. [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
  12. [Fri98]
    Fribourg, L.: A closed-form evaluation for extended timed automata. Research Report LSV-98-2, LSV (March 1998)Google Scholar
  13. [Hen96]
    Henzinger, T.A.: The theory of hybrid automata. In: Proc. 11th Annual Symp. on Logic in Computer Science (LICS), pp. 278–292. IEEE Computer Society Press, Los Alamitos (1996)CrossRefGoogle Scholar
  14. [LASH]
    The Liège Automata-based Symbolic Handler (LASH), Available at:
  15. [Rev93]
    Revesz, P.Z.: A closed-form evaluation for datalog queries with integer (gap)- order constraints. Theor. Comp. Sc. 116(1&2), 117–149 (1993)MATHCrossRefMathSciNetGoogle Scholar
  16. [Wei99]
    Weispfenning, V.: Mixed real-integer linear quantifier elimination. In: ISSAC: Proceedings of the ACM SIGSAM Int. Symp. on Symbolic and Algebraic Computation, Vancouver, pp. 129–136. ACM Press, New York (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Bernard Boigelot
    • 1
  • Frédéric Herbreteau
    • 2
  1. 1.Institut MontefioreB28, Université de LiègeLiègeBelgium
  2. 2.LaBRITalence CedexFrance

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