Test Coverage for Continuous and Hybrid Systems

  • Tarik Nahhal
  • Thao Dang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4590)


We propose a novel test coverage measure for continuous and hybrid systems, which is defined using the star discrepancy notion. We also propose a test generation method guided by this coverage measure. This method was implemented in a prototype tool that can handle high dimensional systems (up to 100 dimensions).


Hybrid System Coverage Measure Star Discrepancy Test Coverage 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.


  1. 1.
    Beck, J., Chen, W.W.L.: Irregularities of Distribution. Cambridge Univ. Press, Cambridge (1987)zbMATHGoogle Scholar
  2. 2.
    Dang, T., Nahhal, T.: Randomized simulation of hybrid systems. Technical report, Verimag, IMAG (May 2006)Google Scholar
  3. 3.
    LaValle, S.M., Branicky, M.S., Lindemann, S.R.: On the relationship between classical grid search and probabilistic roadmaps. Intl. Journal of Robotics Research 23(7-8), 673–692 (2004)CrossRefGoogle Scholar
  4. 4.
    Branicky, M.S., Curtiss, M.M., Levine, J., Morgan, S.: Sampling-based reachability algorithms for control and verification of complex systems. In: Proc. Thirteenth Yale Workshop on Adaptive and Learning Systems, New Haven, CT (2005)Google Scholar
  5. 5.
    Esposito, J.M., Kim, J., Kumar, V.: Adaptive RRTs for validating hybrid robotic control systems. In: Int. Workshop on the Algorithmic Founddations of Robotics (2004)Google Scholar
  6. 6.
    Bhatia, A., Frazzoli, E.: Incremental Search Methods for Reachability Analysis of Continuous and Hybrid Systems. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 142–156. Springer, Heidelberg (2004)Google Scholar
  7. 7.
    Dobkin, D., Eppstein, D.: Computing the discrepancy. In: Proceedings of the Ninth Annual Symposium on Computational Geometry, pp. 47–52 (1993)Google Scholar
  8. 8.
    LaValle, S.M., Kuffner, J.J.: Rapidly-exploring random trees: Progress and prospects. In: Algorithmic and Computational Robotics: New Directions, pp. 293–308. AK Peters, Wellesley, MA (2001)Google Scholar
  9. 9.
    Lee, D., Yannakakis, M.: Principles and Methods of Testing Finite State Machines - A Survey. In: Proceedings of the IEEE 84 (1996)Google Scholar
  10. 10.
    Thiémard, E.: An algorithm to compute bounds for the star discrepancy. J. Complexity 17(4), 850 (2001)zbMATHCrossRefGoogle Scholar
  11. 11.
    Mitchell, I., Tomlin, C.: Level Set Methods for Computation in Hybrid Systems. In: Lynch, N.A., Krogh, B.H. (eds.) HSCC 2000. LNCS, vol. 1790, Springer, Heidelberg (2000)Google Scholar
  12. 12.
    Nahhal, T., Dang, T.: Guided randomized simulation. In: HSCC. LNCS, Springer, Heidelberg (2007)Google Scholar
  13. 13.
    Tan, L., Kim, J., Sokolsky, O., Lee, I.: Model-based Testing and Monitoring for Hybrid Embedded Systems. In: IRI, pp. 487–492 (2004)Google Scholar
  14. 14.
    Tretmans, J.: Testing Concurrent Systems: A Formal Approach. In: Baeten, J.C.M., Mauw, S. (eds.) CONCUR 1999. LNCS, vol. 1664, Springer, Heidelberg (1999)Google Scholar
  15. 15.
    Yershova, A., Jaillet, L., Simeon, T., LaValle, S.M.: Dynamic-domain RRTs: Efficient exploration by controlling the sampling domain. In: Proc. IEEE International Conference on Robotics and Automation, IEEE Computer Society Press, Los Alamitos (2005)Google Scholar
  16. 16.
    Zhu, H., Hall, P.A.V., May, J.H.R.: Software Unit Test Coverage and Adequacy. ACM Computing Surveys 29(4) (December 1997)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Tarik Nahhal
    • 1
  • Thao Dang
    • 1
  1. 1.VERIMAG, 2 avenue de Vignate, 38610 GièresFrance

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