Time Robustness in MTL and Expressivity in Hybrid System Falsification

  • Takumi Akazaki
  • Ichiro Hasuo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9207)


Building on the work by Fainekos and Pappas and the one by Donzé and Maler, we introduce \(\mathbf{AvSTL }\), an extension of metric interval temporal logic by averaged temporal operators. Its expressivity in capturing both space and time robustness helps solving falsification problems (searching for a critical path in hybrid system models); it does so by communicating a designer’s intention more faithfully to the stochastic optimization engine employed in a falsification solver. We also introduce a sliding window-like algorithm that keeps the cost of computing truth/robustness values tractable.


Space Robustness Temporal Logic Stochastic Optimization Formal Verification Automatic Transmission 
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.



Thanks are due to Georgios Fainekos, Tomoyuki Kaga, Toshiki Kataoka, Hisashi Miyashita, Kohei Suenaga and Tomoya Yamaguchi for helpful discussions. The authors are supported by Grant-in-Aid for Young Scientists (A) No. 24680001, JSPS; and T.A. is supported by Grant-in-Aid for JSPS Fellows.


  1. 1.
    TaLiRo-tools. Accessed 26 January 2015
  2. 2.
    Abbas, H., Hoxha, B., Fainekos, G.E., Deshmukh, J.V., Kapinski, J., Ueda, K.: Conformance testing as falsification for cyber-physical systems. In: CoRR, abs/1401.5200 (2014)Google Scholar
  3. 3.
    Abbas, H., Hoxha, B., Fainekos, G.E., Deshmukh, J.V., Kapinski, J., Ueda, K.: Wip abstract: conformance testing as falsification for cyber-physical systems. In: ACM/IEEE International Conference on Cyber-Physical Systems, ICCPS, Berlin, Germany, April 14–17, 2014, pp. 211. IEEE Computer Society (2014)Google Scholar
  4. 4.
    Akazaki, T., Hasuo, I.: Time robustness in MTL and expressivity in hybrid system falsification (extended version) (2015).
  5. 5.
    Almagor, S., Boker, U., Kupferman, O.: Discounting in LTL. In: Ábrahám, E., Havelund, K. (eds.) TACAS 2014 (ETAPS). LNCS, vol. 8413, pp. 424–439. Springer, Heidelberg (2014) CrossRefGoogle Scholar
  6. 6.
    Alur, R., Feder, T., Henzinger, T.A.: The benefits of relaxing punctuality. J. ACM 43(1), 116–146 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Annpureddy, Y., Liu, C., Fainekos, G., Sankaranarayanan, S.: S-TaLiRo: a tool for temporal logic falsification for hybrid systems. In: Abdulla, P.A., Leino, K.R.M. (eds.) TACAS 2011. LNCS, vol. 6605, pp. 254–257. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  8. 8.
    Bouyer, P., Fahrenberg, U., Larsen, K.G., Markey, N., Srba, J.: Infinite runs in weighted timed automata with energy constraints. In: Cassez, F., Jard, C. (eds.) FORMATS 2008. LNCS, vol. 5215, pp. 33–47. Springer, Heidelberg (2008) CrossRefGoogle Scholar
  9. 9.
    Brenguier, R., Cassez, F., Raskin, J.-F.: Energy and mean-payoff timed games. In: Fränzle, M., Lygeros, J. (eds.) Proceedings of the 17th International Conference on Hybrid Systems: Computation and Control, pp. 283–292. ACM, New York (2014)Google Scholar
  10. 10.
    Chatterjee, K., Henzinger, T.A., Jurdzinski, M.: Mean-payoff parity games. In: 20th IEEE Symposium on Logic in Computer Science, LICS, 26–29 June 2005, Chicago, IL, USA, pp. 178–187. IEEE Computer Society (2005)Google Scholar
  11. 11.
    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
  12. 12.
    Donzé, A., Ferrère, T., Maler, O.: Efficient robust monitoring for STL. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 264–279. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  13. 13.
    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
  14. 14.
    Ehrenfeucht, A., Mycielski, J.: Positional strategies for mean payoff games. Int. J. Game Theor. 8(2), 109–113 (1979)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Fainekos, G.E., Sankaranarayanan, S., Ueda, K., Yazarel, H.: Verification of automotive control applications using S-TaLiRo. Am. Control Conf. (ACC) 2012, 3567–3572 (2012)zbMATHGoogle Scholar
  16. 16.
    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
  17. 17.
    Fränzle, M., Lygeros, J. (eds.) 17th International Conference on Hybrid Systems: Computation and Control (part of CPS Week), HSCC 2014, Berlin, Germany, April 15–17, 2014. ACM (2014)Google Scholar
  18. 18.
    Hoxha, B., Abbas, H., Fainekos, G.: Benchmarks for temporal logic requirements for automotive systems. In: Proceedings of Applied Verification for Continuous and Hybrid Systems (2014)Google Scholar
  19. 19.
    Jin, X., Deshmukh, J.V., Kapinski, J., Ueda, K., Butts, K.: Powertrain control verification benchmark. In: Fränzle, M., Lygeros, J. (eds.) Proceedings of the 17th international conference on Hybrid systems: computation and control, pp. 253–262. ACM, New York (2014)Google Scholar
  20. 20.
    Jin, X., Donzé, A., Deshmukh, J.V., Seshia, S.A.: Mining requirements from closed-loop control models. In: Belta, C., Ivancic, F. (eds.) Proceedings of the 16th International Conference on Hybrid Systems: Computation and Control, HSCC 2013, pp. 43–52. ACM, New York (2013)Google Scholar
  21. 21.
    Kong, Z., Jones, A., Ayala, A.M., Gol, E.A., Belta, C.: Temporal logic inference for classification and prediction from data. In: Fränzle, M., Lygeros, J. (eds.) Proceedings of the 17th international conference on Hybrid systems: computation and control, pp. 273–282. ACM, New York (2014)Google Scholar
  22. 22.
    Lemire, D.: Streaming maximum-minimum filter using no more than three comparisons per element. Nord. J. Comput. 13(4), 328–339 (2006)MathSciNetzbMATHGoogle Scholar
  23. 23.
    Maler, O., Nickovic, D.: Monitoring temporal properties of continuous signals. In: Lakhnech, Y., Yovine, S. (eds.) FORMATS 2004 and FTRTFT 2004. LNCS, vol. 3253, pp. 152–166. Springer, Heidelberg (2004) CrossRefGoogle Scholar
  24. 24.
    Sankaranarayanan, S., Fainekos, G.: Falsification of temporal properties of hybrid systems using the cross-entropy method. In: Proceedings of the 15th ACM International Conference on Hybrid Systems: Computation and Control, HSCC 2012, pp. 125–134. ACM, New York, NY, USA (2012)Google Scholar
  25. 25.
    Yang, H., Hoxha, B., Fainekos, G.: Querying parametric temporal logic properties on embedded systems. In: Nielsen, B., Weise, C. (eds.) ICTSS 2012. LNCS, vol. 7641, pp. 136–151. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  26. 26.
    Zutshi, A., Deshmukh, J.V., Sankaranarayanan, S., Kapinski, J.: Multiple shooting, cegar-based falsification for hybrid systems. In: Proceedings of the 14th International Conference on Embedded Software, EMSOFT 2014, pp. 5:1–5:10, ACM, New York, NY, USA (2014)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.The University of TokyoTokyoJapan
  2. 2.JSPS Research FellowTokyoJapan

Personalised recommendations