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A Counterexample-Guided Approach to Parameter Synthesis for Linear Hybrid Automata

  • Goran Frehse
  • Sumit Kumar Jha
  • Bruce H. Krogh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4981)

Abstract

Our goal is to find the set of parameters for which a given linear hybrid automaton does not reach a given set of bad states. The problem is known to be semi-solvable (if the algorithm terminates the result is correct) by introducing the parameters as state variables and computing the set of reachable states. This is usually too expensive, however, and in our experiments only possible for very simple systems with few parameters. We propose an adaptation of counterexample-guided abstraction refinement (CEGAR) with which one can obtain an underapproximation of the set of good parameters using linear programming. The adaptation is generic and can be applied on top of any CEGAR method where the counterexamples correspond to paths in the concrete system. For each counterexample, the cost incurred by underapproximating the parameters is polynomial in the number of variables, parameters, and the length of counterexample. We identify a syntactic condition for which the approach is complete in the sense that the underapproximation is empty only if the problem has no solution. Experimental results are provided for two CEGAR methods, a simple discrete version and iterative relaxation abstraction (IRA), both of which show a drastic improvement in performance compared to standard reachability.

Keywords

Linear Constraint Good Parameter Reachable State Parameter Synthesis Feasible Path 
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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References

  1. 1.
    Henzinger, T.A., Wong-Toi, H.: Using HyTech to synthesize control parameters for a steam boiler. In: Abrial, J.-R., Börger, E., Langmaack, H. (eds.) Dagstuhl Seminar 1995. LNCS, vol. 1165, pp. 265–282. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  2. 2.
    Clarke, E.M., Grumberg, O., Jha, S., Lu, Y., Veith, H.: 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
  3. 3.
    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, Springer, Heidelberg (2007)CrossRefGoogle Scholar
  4. 4.
    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
  5. 5.
    Li, X., Jha, S.K., Bu, L.: Towards an Efficient Path-Oriented Tool for Bounded Reachability analysis of Linear Hybrid Systems using Linear Programming. In: BMC 2006: Proceedings of the Workshop on Bounded Model Checking (2006)Google Scholar
  6. 6.
    Segelken, M.: Abstraction and counterexample-guided construction of ω-automata for model checking of step-discrete linear hybrid models. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 433–448. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  7. 7.
    Horowitz, R., Varaiya, P.: Control design of an automated highway system. Proc. IEEE 88, 913–925 (2000)CrossRefGoogle Scholar
  8. 8.
    GNU Linear Programming Kit, v.4.17 (2007), http://www.gnu.org/software/glpk
  9. 9.

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Goran Frehse
    • 1
  • Sumit Kumar Jha
    • 2
  • Bruce H. Krogh
    • 3
  1. 1.Verimag (UJF-CNRS-INPG)GièresFrance
  2. 2.Computer Science DepartmentCarnegie Mellon University 
  3. 3.ECE DepartmentCarnegie Mellon UniversityPittsburghUSA

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