Reachability for Linear Hybrid Automata Using Iterative Relaxation Abstraction

  • Sumit K. Jha
  • Bruce H. Krogh
  • James E. Weimer
  • Edmund M. Clarke
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4416)


This paper introduces iterative relaxation abstraction (IRA), a new method for reachability analysis of LHA that aims to improve scalability by combining the capabilities of current tools for analysis of low-dimensional LHA with the power of linear programming (LP) for large numbers of constraints and variables. IRA is inspired by the success of counterexample guided abstraction refinement (CEGAR) techniques in verification of discrete systems. On each iteration, a low-dimensional LHA called a relaxation abstraction is constructed using a subset of the continuous variables from the original LHA. Hybrid system reachability analysis then generates a regular language called the discrete path abstraction containing all possible counterexamples (paths to the bad locations) in the relaxation abstraction. If the discrete path abstraction is non-empty, a particular counterexample is selected and LP infeasibility analysis determines if the counterexample is spurious using the constraints along the path from the original high-dimensional LHA. If the counterexample is spurious, LP techniques identify an irreducible infeasible subset (IIS) of constraints from which the set of continuous variables is selected for the the construction of the next relaxation abstraction. IRA stops if the discrete path abstraction is empty or a legitimate counterexample is found. The effectiveness of the approach is illustrated with an example.


Model Check Hybrid System Linear Constraint Regular Language Hybrid Automaton 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Henzinger, T.: The Theory of Hybrid Automata. In: Logic in Computer Science, p. 278 (1996)Google Scholar
  2. 2.
    Alur, R., et al.: The algorithmic analysis of hybrid systems. Theoretical Computer Science 138(1), 3–34 (1995), zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Henzinger, T.A., Ho, P.-H., Wong-Toi, H.: HyTech: A model checker for hybrid systems. International Journal on Software Tools for Technology Transfer 1(1–2), 110–122 (1997), zbMATHGoogle Scholar
  4. 4.
    Alur, R., Henzinger, T., Wong-Toi, H.: Symbolic analysis of hybrid systems. In: Proc. 37-th IEEE Conference on Decision and Control, IEEE Computer Society Press, Los Alamitos (1997), Google Scholar
  5. 5.
    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)Google Scholar
  6. 6.
    Kurshan, R.: Computer-aided Verification of Coordinating Processes: The Automata Theoretic Approach. Princeton University Press, Princeton (1994)Google Scholar
  7. 7.
    Clarke, E.M., et al.: Counterexample-guided abstraction refinement. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 154–169. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  8. 8.
    Ball, T., et al.: Automatic Predicate Abstraction of C Programs. In: SIGPLAN Conference on Programming Language Design and Implementation, pp. 203–213 (2001),
  9. 9.
    Clarke, E.M., Grumberg, O., Peled, D.A.: Model Checking. MIT Press, Cambridge (1999)Google Scholar
  10. 10.
    Zhang, L., Malik, S.: Validating SAT Solvers Using an Independent Resolution-Based Checker: Practical Implementations and Other Applications. In: DATE, pp. 10880–10885. IEEE Computer Society, Los Alamitos (2003)Google Scholar
  11. 11.
    Chaki, S., et al.: Predicate abstraction with minimum predicates. In: Geist, D., Tronci, E. (eds.) CHARME 2003. LNCS, vol. 2860, Springer, Heidelberg (2003)Google Scholar
  12. 12.
    Li, X., Jha, S.K., Bu, L.: Towards an Efficient Path-Oriented Tool for Bounded Reachability analysis of Linear Hybrid Systems using Linear Programming (2006)Google Scholar
  13. 13.
    Chinneck, J., Dravnieks, E.: Locating minimal infeasible constraint sets in linear programs. ORSA Journal on Computing 3, 157–168 (1991)zbMATHGoogle Scholar
  14. 14.
    Dantzig, G.B., Eaves, B.C.: Fourier-Motzkin elimination and Its Dual. J. Comb. Theory, Ser. A 14(3), 288–297 (1973)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Sankaran, J.K.: A note on resolving infeasibility in linear programs by constraint relaxation. Operations Research Letters 13, 19–20 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Chinneck, J.W.: MINOS(IIS): Infeasibility analysis using MINOS. Comput. Oper. Res. 21(1), 1–9 (1994)zbMATHCrossRefGoogle Scholar
  17. 17.
  18. 18.
    Hung, M.S., Rom, W.O., Waren, A.D.: Optimization with IBM OSL and Handbook for IBM OSL (1993)Google Scholar
  19. 19.
  20. 20.
    Ho, P.H.: Automatic Analysis of Hybrid Systems, Ph.D. thesis, technical report CSD-TR95-1536, Cornell University (August 1995)Google Scholar
  21. 21.
    Mohri, M., Pereira, F., Riley, M.: The design principles of a weighted finite-state transducer library. Theoretical Computer Science 231(1), 17–32 (2000), zbMATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Jiang, S.: Reachability analysis of Linear Hybrid Automata by using counterexample fragment based abstraction refinement. Submitted (2006)Google Scholar
  23. 23.
    Karmarkar, N.: A new polynomial-time algorithm for linear programming. Combinatorica 4(4), 373–395 (1984)zbMATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Fehnker, A., et al.: Refining Abstractions of Hybrid Systems Using Counterexample Fragments. In: Morari, M., Thiele, L. (eds.) HSCC 2005. LNCS, vol. 3414, pp. 242–257. Springer, Heidelberg (2005)Google Scholar
  25. 25.
    Alur, R., Dang, T., Ivancic, F.: Counterexample-guided predicate abstraction of hybrid systems. Theor. Comput. Sci. 354(2), 250–271 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    Morari, M., Thiele, L. (eds.): HSCC 2005. LNCS, vol. 3414. Springer, Heidelberg (2005)zbMATHGoogle Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Sumit K. Jha
    • 1
  • Bruce H. Krogh
    • 2
  • James E. Weimer
    • 2
  • Edmund M. Clarke
    • 1
  1. 1.Computer Science Department, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213USA
  2. 2.ECE Department, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA15213USA

Personalised recommendations