Time-Bounded Reachability for Monotonic Hybrid Automata: Complexity and Fixed Points

  • Thomas Brihaye
  • Laurent Doyen
  • Gilles Geeraerts
  • Joel Ouaknine
  • Jean-Francois Raskin
  • James Worrell
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8172)


We study the time-bounded reachability problem for monotonic hybrid automata (MHA), i.e., rectangular hybrid automata for which the rate of each variable is either always non-negative or always non-positive. In this paper, we revisit the decidability results presented in [5] and show that the problem is NExpTime-complete. We also show that we can effectively compute fixed points that characterise the sets of states that are reachable (resp. co-reachable) within T time units from a given state.


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  1. 1.
    Alur, R., Courcoubetis, C., Henzinger, T.A., Ho, P.-H.: Hybrid automata: An algorithmic approach to the specification and verification of hybrid systems. In: Grossman, R.L., Ravn, A.P., Rischel, H., Nerode, A. (eds.) HS 1991 and HS 1992. LNCS, vol. 736, Springer, Heidelberg (1993)CrossRefGoogle Scholar
  2. 2.
    Alur, R., Dill, D.: A theory of timed automata. TTCS 126(2), 183–235 (1994)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Bagnara, R., Hill, P.M., Zaffanella, E.: The parma polyhedra library: Toward a complete set of numerical abstractions for the analysis and verification of hardware and software systems. Sci. Comput. Program. 72(1-2) (2008)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Basu, S.: New results on quantifier elimination over real closed fields and applications to constraint databases. J. ACM 46(4) (1999)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Brihaye, T., Doyen, L., Geeraerts, G., Ouaknine, J., Raskin, J.-F., Worrell, J.: On reachability for hybrid automata over bounded time. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011, Part II. LNCS, vol. 6756, pp. 416–427. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  6. 6.
    Brihaye, T., Doyen, L., Geeraerts, G., Ouaknine, J., Raskin, J.-F., Worrell, J.: Time-bounded reachability for hybrid automata: Complexity and fixpoints. Technical report CoRR abs/1211.1276, Cornell University Library, (2012),
  7. 7.
    Henzinger, T.A.: The theory of hybrid automata. In: LICS 1996. IEEE Computer Society (1996)Google Scholar
  8. 8.
    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)CrossRefGoogle Scholar
  9. 9.
    Henzinger, T.A., Ho, P.-H., Wong-Toi, H.: Hytech: A model checker for hybrid systems. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 460–463. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  10. 10.
    Henzinger, T.A., Kopke, P.W., Puri, A., Varaiya, P.: What’s decidable about hybrid automata. JCSS 57(1), 94–124 (1998)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Henzinger, T.A., Majumdar, R., Raskin, J.-F.: A classification of symbolic transition systems. ACM Trans. Comput. Log. 6(1), 1–32 (2005)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Jenkins, M., Ouaknine, J., Rabinovich, A., Worrell, J.: Alternating timed automata over bounded time. In: LICS 2010. IEEE Computer Society (2010)Google Scholar
  13. 13.
    Jha, S.K., Krogh, B.H., Weimer, J.E., Clarke, E.M.: Reachability for linear hybrid automata using iterative relaxation abstraction. In: Bemporad, A., Bicchi, A., Buttazzo, G. (eds.) HSCC 2007. LNCS, vol. 4416, pp. 287–300. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  14. 14.
    Ouaknine, J., Rabinovich, A., Worrell, J.: Time-bounded verification. In: Bravetti, M., Zavattaro, G. (eds.) CONCUR 2009. LNCS, vol. 5710, pp. 496–510. Springer, Heidelberg (2009)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Thomas Brihaye
    • 1
  • Laurent Doyen
    • 2
  • Gilles Geeraerts
    • 3
  • Joel Ouaknine
    • 4
  • Jean-Francois Raskin
    • 3
  • James Worrell
    • 4
  1. 1.UMonsBelgium
  2. 2.LSV CachanFrance
  3. 3.ULBBelgium
  4. 4.Oxford UniversityUK

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