On Timed Simulation Relations for Hybrid Systems and Compositionality

  • Goran Frehse
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4202)


Timed and weak timed simulation relations are often used to show that operations on hybrid systems result in equivalent behavior or in conservative overapproximations. Given that systems are frequently designed and verified in a modular approach, it is desirable that this relationship is compositional, which is not the case for hybrid systems in general. We identify subclasses of linear hybrid automata that are compositional with respect to timed, respectively weak timed simulation.


Hybrid System Target State External Variable Hybrid Automaton Simulation Relation 
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  1. 1.
    Henzinger, T.A., Pei-Hsin, H., Wong-Toi, H.: Algorithmic analysis of nonlinear hybrid systems. IEEE Trans. Automatic Control 43(4), 540–554 (1998)zbMATHCrossRefGoogle Scholar
  2. 2.
    Frehse, G.: PHAVer: Algorithmic verification of hybrid systems past HyTech. In: Morari, M., Thiele, L. (eds.) HSCC 2005. LNCS, vol. 3414, pp. 258–273. Springer, Heidelberg (2005), PHAVer is available at: CrossRefGoogle Scholar
  3. 3.
    Doyen, L., Henzinger, T.A., Raskin, J.-F.: Automatic rectangular refinement of affine hybrid systems. In: Pettersson, P., Yi, W. (eds.) FORMATS 2005. LNCS, vol. 3829, pp. 144–161. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  4. 4.
    Alur, R., Courcoubetis, C., Halbwachs, N., Henzinger, T.A., Pei-Hsin, H., Nicollin, X., Olivero, A., Sifakis, J., Yovine, S.: The algorithmic analysis of hybrid systems. Theor. Comp. Science 138(1), 3–34 (1995)zbMATHCrossRefGoogle Scholar
  5. 5.
    Ábrahám-Mumm, E., Hannemann, U., Steffen, M.: Verification of hybrid systems: Formalization and proof rules in PVS. In: Proc. IEEE Int. Conf. on Engineering of Complex Computer Systems (ICECCS 2001) (June 2001)Google Scholar
  6. 6.
    Lynch, N.A., Segala, R., Vaandrager, F.W.: Hybrid I/O automata. Information and Computation 185(1), 105–157 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Henzinger, T.A.: The theory of hybrid automata. In: Proc. 11th Annual IEEE Symposium on Logic in Computer Science, LICS 1996, New Brunswick, New Jersey, July 27-30, 1996, pp. 278–292. IEEE Computer Society Press, Los Alamitos (1996)CrossRefGoogle Scholar
  8. 8.
    Frehse, G., Han, Z., Krogh, B.H.: Assume-guarantee reasoning for hybrid i/o-automata by over-approximation of continuous interaction. In: Proc. IEEE Conf. Decision & Control (CDC 2004), Atl., Bahamas, December 14–17 (2004)Google Scholar
  9. 9.
    Frehse, G.: Compositional verification of hybrid systems with discrete interaction using simulation relations. In: Proc. IEEE Conf. Computer-Aided Control System Design (CACSD 2004), Taipei, Taiwan, September 1-4 (2004)Google Scholar
  10. 10.
    Frehse, G.: Compositional Verification of Hybrid Systems using Simulation Relations. PhD thesis, Radboud Universiteit Nijmegen (October 2005)Google Scholar
  11. 11.
    Lynch, N.A., Fischer, M.J.: On describing the behavior and implementation of distributed systems. Theoretical Computer Science 13(1), 17–43 (1981); Special issue on Semantics of Concurrent ComputationzbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Alur, R., Henzinger, T.A., Pei-Hsin, H.: Automatic symbolic verification of embedded systems. IEEE Trans. Soft. Engineering 22, 181–201 (1996)CrossRefGoogle Scholar
  13. 13.
    Henzinger, T.A., Wong-Toi, H.: Linear phase-portrait approximations for nonlinear hybrid systems. In: Alur, R., Sontag, E.D., Henzinger, T.A. (eds.) HS 1995. LNCS, vol. 1066, pp. 377–388. Springer, Heidelberg (1996)CrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Goran Frehse
    • 1
  1. 1.VERIMAG 

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