Stochastic Local Search for Falsification of Hybrid Systems

  • Jyotirmoy DeshmukhEmail author
  • Xiaoqing Jin
  • James Kapinski
  • Oded Maler
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9364)


Falsification techniques for models of embedded control systems automate the process of testing models to find bugs by searching for model-inputs that violate behavioral specifications given by logical and quantitative correctness requirements. A recent advance in falsification is to encode property satisfaction as a cost function based on a finite parameterization of the (bounded-time) input signal, which allows formulating bug-finding as an optimization problem. In this paper, we present a falsification technique that uses a local search technique called Tabu search to search for optimal inputs. The key idea is to discretize the space of input signals and use the Tabu list to avoid revisiting previously encountered input signals. As local search techniques may converge to local optima, we introduce stochastic aspects such as random restarts, sampling and probabilistically picking suboptimal inputs to guide the technique towards a global optimum. Picking the right parameterization of the input space is often challenging for designers, so we allow dynamic refinement of the input space as the search progresses. We implement the technique in a tool called sitar, and show scalability of the technique by using it to falsify requirements on an early prototype of an industrial-sized automotive powertrain control design.


Local Search Tabu Search Temporal Logic Input Space Input Sequence 
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.



The authors would like to thank the anonymous reviewers for constructive feedback that helped improve this paper.


  1. 1.
    Abbas, H., Fainekos, G.: Linear hybrid system falsification through local search. In: Bultan, T., Hsiung, P.-A. (eds.) ATVA 2011. LNCS, vol. 6996, pp. 503–510. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  2. 2.
    Annapureddy, Y.S.R., Fainekos, G.E.: Ant Colonies for Temporal Logic Falsification of Hybrid Systems. In: Proceedings of the IECON, pp. 91–96 (2010)Google Scholar
  3. 3.
    Annapureddy, Y.S.R., Liu, C., Fainekos, G.E., Sankaranarayanan, S.: S-TaLiRo: a tool for temporal logic falsification for hybrid systems. In: Proceedings of the Tools and Algorithms for the Construction and Analysis of Systems, pp. 254–257 (2011)Google Scholar
  4. 4.
    Asarin, E., Maler, O.: Achilles and the tortoise climbing up the arithmetical hierarchy. JCSS 57(3), 389–398 (1998)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Hoxha, H.A.B., Fainekos, G.: Using S-TaLiRo on industrial size automotive models. In: Worskhop on Applied Verification for Continuous and Hybrid Systems (2014)Google Scholar
  6. 6.
    Cordeau, J.-F., Laporte, G., Mercier, A., et al.: A unified tabu search heuristic for vehicle routing problems with time windows. J. Oper. Res. Soc. 52(8), 928–936 (2001)CrossRefzbMATHGoogle Scholar
  7. 7.
    Donzé, A.: Breach, a toolbox for verification and parameter synthesis of hybrid systems. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 167–170. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  8. 8.
    Donzé, A., Maler, O.: Robust satisfaction of temporal logic over real-valued signals. In: Chatterjee, K., Henzinger, T.A. (eds.) FORMATS 2010. LNCS, vol. 6246, pp. 92–106. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  9. 9.
    Dreossi, T., Dang, T., Donzé, A., Kapinski, J., Jin, X., Deshmukh, J.V.: Efficient guiding strategies for testing of temporal properties of hybrid systems. In: Havelund, K., Holzmann, G., Joshi, R. (eds.) NFM 2015. LNCS, vol. 9058, pp. 127–142. Springer, Heidelberg (2015) Google Scholar
  10. 10.
    Fainekos, G.E., Pappas, G.J.: Robustness of temporal logic specifications for continuous-time signals. Theor. Comput. Sci. 410(42), 4262–4291 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Henzinger, T., Kopke, P., Puri, A., Varaiya, P.: What’s Decidable about Hybrid Automata?. In: Proceedings of the Symposium on Theory of Computing, pp. 373–382 (1995)Google Scholar
  12. 12.
    Jin, X., Deshmukh, J.V., Kapinski, J., Ueda, K., Butts, K.: Powertrain Control Verification Benchmark. In: Proceeding of Hybrid Systems: Computation and Control, pp. 253–262 (2014)Google Scholar
  13. 13.
    Kirkpatrick, S., Vecchi, M., et al.: Optimization by simmulated annealing. Science 220(4598), 671–680 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Kuřátko, J., Ratschan, S.: Combined global and local search for the falsification of hybrid systems. In: Legay, A., Bozga, M. (eds.) FORMATS 2014. LNCS, vol. 8711, pp. 146–160. Springer, Heidelberg (2014) Google Scholar
  15. 15.
    Nghiem, T., Sankaranarayanan, S., Fainekos, G.E., Ivancic, F., Gupta, A., Pappas, G.J.: Monte-carlo techniques for falsification of temporal properties of non-linear hybrid systems. In: Proceeding of Hybrid Systems: Computation and Control, pp. 211–220 (2010)Google Scholar
  16. 16.
    Plaku, E., Kavraki, L.E., Vardi, M.Y.: Hybrid systems: from verification to falsification by combining motion planning and discrete search. Formal Methods Sys. Design 34(2), 157–182 (2009)CrossRefzbMATHGoogle Scholar
  17. 17.
    Plaku, E., Kavraki, L.E., Vardi, M.Y.: Falsification of ltl safety properties in hybrid systems. Softw. Tools Technol. Transfer 15(4), 305–320 (2013)CrossRefzbMATHGoogle Scholar
  18. 18.
    Sankaranarayanan, S., Fainekos, G.E.: Falsification of temporal properties of hybrid systems using the cross-entropy method. Computation and Control. In: Proceeding of Hybrid Systems (2012)Google Scholar
  19. 19.
    Spall, J.C.: Introduction to Stochastic Search and Optimization, 1st edn. Wiley, New York (2003)CrossRefzbMATHGoogle Scholar
  20. 20.
    Zutshi, A., Sankaranarayanan, S., Deshmukh, J.V., Kapinski, J.: Multiple shooting, cegar-based falsification for hybrid systems. In: Proceedings of the 14th International Conference on Embedded Software, p. 5 (2014)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Jyotirmoy Deshmukh
    • 1
    Email author
  • Xiaoqing Jin
    • 1
  • James Kapinski
    • 1
  • Oded Maler
    • 2
  1. 1.Toyota Technical CenterGardenaUSA
  2. 2.VerimagGièresFrance

Personalised recommendations