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Online Quantitative Timed Pattern Matching with Semiring-Valued Weighted Automata

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Formal Modeling and Analysis of Timed Systems (FORMATS 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11750))

Abstract

Monitoring of a signal plays an essential role in the runtime verification of cyber-physical systems. Qualitative timed pattern matching is one of the mathematical formulations of monitoring, which gives a Boolean verdict for each sub-signal according to the satisfaction of the given specification. There are two orthogonal directions of extension of the qualitative timed pattern matching. One direction on the result is quantitative: what engineers want is often not a qualitative verdict but the quantitative measurement of the satisfaction of the specification. The other direction on the algorithm is online checking: the monitor returns some verdicts before obtaining the entire signal, which enables to monitor a running system. It is desired from application viewpoints. In this paper, we conduct these two extensions, taking an automata-based approach. This is the first quantitative and online timed pattern matching algorithm to the best of our knowledge. More specifically, we employ what we call timed symbolic weighted automata to specify quantitative specifications to be monitored, and we obtain an online algorithm using the shortest distance of a weighted variant of the zone graph and dynamic programming. Moreover, our problem setting is semiring-based and therefore, general. Our experimental results confirm the scalability of our algorithm for specifications with a time-bound.

Thanks are due to Ichiro Hasuo for a lot of useful comments and Sasinee Pruekprasert for a feedback. This work is partially supported by JST ERATO HASUO Metamathematics for Systems Design Project (No. JPMJER1603) and by JSPS Grants-in-Aid No. 15KT0012 & 18J22498.

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Notes

  1. 1.

    The choice of \(\tilde{\nu }\) and \(\tilde{\nu }'\) does not change \(\sigma (\tilde{\nu }(T))\) and \(\sigma (\tilde{\nu }'(T))\) due to the definition of \(Q^{\mathrm {sym}}\).

References

  1. tprasadtp/cruise-control-simulink: Simulink model for Cruise control system of a car with dynamic road conditions. https://github.com/tprasadtp/cruise-control-simulink

  2. Akazaki, T., Hasuo, I.: Time robustness in MTL and expressivity in hybrid system falsification. In: Kroening, D., Păsăreanu, C.S. (eds.) CAV 2015. LNCS, vol. 9207, pp. 356–374. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21668-3_21

    Chapter  Google Scholar 

  3. Alur, R., Dill, D.L.: A theory of timed automata. Theor. Comput. Sci. 126(2), 183–235 (1994). https://doi.org/10.1016/0304-3975(94)90010-8

    Article  MathSciNet  MATH  Google Scholar 

  4. André, É., Hasuo, I., Waga, M.: Offline timed pattern matching under uncertainty. In: 23rd International Conference on Engineering of Complex Computer Systems, ICECCS 2018, Melbourne, Australia, December 12–14, 2018, pp. 10–20. IEEE Computer Society (2018). https://doi.org/10.1109/ICECCS2018.2018.00010

  5. 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). https://doi.org/10.1007/978-3-642-19835-9_21

    Chapter  MATH  Google Scholar 

  6. Asarin, E., Caspi, P., Maler, O.: A Kleene theorem for timed automata. In: Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science, Warsaw, Poland, June 29 - July 2, 1997, pp. 160–171. IEEE Computer Society (1997). https://doi.org/10.1109/LICS.1997.614944

  7. Bakhirkin, A., Ferrère, T., Maler, O., Ulus, D.: On the quantitative semantics of regular expressions over real-valued signals. In: Abate, A., Geeraerts, G. (eds.) FORMATS 2017. LNCS, vol. 10419, pp. 189–206. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-65765-3_11

    Chapter  MATH  Google Scholar 

  8. Bakhirkin, A., Ferrère, T., Nickovic, D., Maler, O., Asarin, E.: Online timed pattern matching using automata. In: Jansen, D.N., Prabhakar, P. (eds.) FORMATS 2018. LNCS, vol. 11022, pp. 215–232. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-00151-3_13

    Chapter  MATH  Google Scholar 

  9. Bartocci, E., Majumdar, R. (eds.): RV 2015. LNCS, vol. 9333. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-23820-3

    Book  Google Scholar 

  10. Bengtsson, J., Yi, W.: Timed automata: semantics, algorithms and tools. In: Desel, J., Reisig, W., Rozenberg, G. (eds.) ACPN 2003. LNCS, vol. 3098, pp. 87–124. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-27755-2_3

    Chapter  MATH  Google Scholar 

  11. Bombara, G., Vasile, C.I., Penedo, F., Yasuoka, H., Belta, C.: A decision tree approach to data classification using signal temporal logic. In: Abate, A., Fainekos, G.E. (eds.) Proceedings of the 19th International Conference on Hybrid Systems: Computation and Control, HSCC 2016, Vienna, Austria, April 12–14, 2016, pp. 1–10. ACM (2016). https://doi.org/10.1145/2883817.2883843

  12. Chatterjee, K., Henzinger, T.A., Otop, J.: Quantitative monitor automata. In: Rival, X. (ed.) SAS 2016. LNCS, vol. 9837, pp. 23–38. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53413-7_2

    Chapter  Google Scholar 

  13. Chen, S., Sokolsky, O., Weimer, J., Lee, I.: Data-driven adaptive safety monitoring using virtual subjects in medical cyber-physical systems: a glucose control case study. JCSE 10(3) (2016). https://doi.org/10.5626/JCSE.2016.10.3.75

    Article  Google Scholar 

  14. Deshmukh, J.V., Donzé, A., Ghosh, S., Jin, X., Juniwal, G., Seshia, S.A.: Robust online monitoring of signal temporal logic. In: Bartocci and Majumdar [9], pp. 55–70. https://doi.org/10.1007/978-3-319-23820-3_4

    Chapter  Google Scholar 

  15. Dill, D.L.: Timing assumptions and verification of finite-state concurrent systems. In: Sifakis, J. (ed.) CAV 1989. LNCS, vol. 407, pp. 197–212. Springer, Heidelberg (1990). https://doi.org/10.1007/3-540-52148-8_17

    Chapter  Google Scholar 

  16. 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). https://doi.org/10.1007/978-3-642-14295-6_17

    Chapter  Google Scholar 

  17. 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). https://doi.org/10.1007/978-3-642-15297-9_9

    Chapter  MATH  Google Scholar 

  18. Droste, M., Kuich, W., Vogler, H.: Handbook of Weighted Automata, 1st edn. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-01492-5

    Book  MATH  Google Scholar 

  19. Fainekos, G.E., Pappas, G.J.: Robustness of temporal logic specifications for continuous-time signals. Theor. Comput. Sci. 410(42), 4262–4291 (2009). https://doi.org/10.1016/j.tcs.2009.06.021

    Article  MathSciNet  MATH  Google Scholar 

  20. Jaksic, S., Bartocci, E., Grosu, R., Nguyen, T., Nickovic, D.: Quantitative monitoring of STL with edit distance. Formal Meth. Syst. Des. 53(1), 83–112 (2018). https://doi.org/10.1007/s10703-018-0319-x

    Article  MATH  Google Scholar 

  21. Jaksic, S., Bartocci, E., Grosu, R., Nickovic, D.: An algebraic framework for runtime verification. IEEE Trans. CAD Integr. Circ. Syst. 37(11), 2233–2243 (2018). https://doi.org/10.1109/TCAD.2018.2858460

    Article  Google Scholar 

  22. Kane, A., Chowdhury, O., Datta, A., Koopman, P.: A case study on runtime monitoring of an autonomous research vehicle (ARV) system. In: Bartocci and Majumdar [9], pp. 102–117. https://doi.org/10.1007/978-3-319-23820-3_7

    Chapter  Google Scholar 

  23. Kapinski, J., et al.: St-lib: a library for specifying and classifying model behaviors. Technical report, SAE Technical Paper (2016)

    Google Scholar 

  24. Maler, O., Nickovic, D.: Monitoring temporal properties of continuous signals. In: Lakhnech, Y., Yovine, S. (eds.) FORMATS/FTRTFT -2004. LNCS, vol. 3253, pp. 152–166. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-30206-3_12

    Chapter  MATH  Google Scholar 

  25. Mohri, M.: Weighted Automata Algorithms. In: Droste, M., Kuich, W., Vogler, H. (eds.) Handbook of Weighted Automata, pp. 213–254. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-01492-5_6

    Chapter  Google Scholar 

  26. Raimondi, F., Skene, J., Emmerich, W.: Efficient online monitoring of web-service slas. In: Harrold, M.J., Murphy, G.C. (eds.) Proceedings of the 16th ACM SIGSOFT International Symposium on Foundations of Software Engineering, 2008, Atlanta, Georgia, USA, November 9–14, 2008, pp. 170–180. ACM (2008). https://doi.org/10.1145/1453101.1453125

  27. Schützenberger, M.P.: On the definition of a family of automata. Inf. Control 4(2–3), 245–270 (1961). https://doi.org/10.1016/S0019-9958(61)80020-X

    Article  MathSciNet  MATH  Google Scholar 

  28. Ulus, D., Ferrère, T., Asarin, E., Maler, O.: Timed pattern matching. In: Legay, A., Bozga, M. (eds.) FORMATS 2014. LNCS, vol. 8711, pp. 222–236. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-10512-3_16

    Chapter  MATH  Google Scholar 

  29. Ulus, D., Ferrère, T., Asarin, E., Maler, O.: Online timed pattern matching using derivatives. In: Chechik, M., Raskin, J.-F. (eds.) TACAS 2016. LNCS, vol. 9636, pp. 736–751. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49674-9_47

    Chapter  Google Scholar 

  30. Veanes, M., Hooimeijer, P., Livshits, B., Molnar, D., Bjørner, N.: Symbolic finite state transducers: algorithms and applications. In: Field, J., Hicks, M. (eds.) Proceedings of the 39th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL 2012, Philadelphia, Pennsylvania, USA, January 22–28, 2012, pp. 137–150. ACM (2012). https://doi.org/10.1145/2103656.2103674

  31. Waga, M.: Online quantitative timed pattern matching with semiring-valued weighted automata. CoRR abs/1906.12133 (2019). http://arxiv.org/abs/1906.12133

  32. Waga, M., Akazaki, T., Hasuo, I.: A boyer-moore type algorithm for timed pattern matching. In: Fränzle, M., Markey, N. (eds.) FORMATS 2016. LNCS, vol. 9884, pp. 121–139. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-44878-7_8

    Chapter  MATH  Google Scholar 

  33. Waga, M., André, É.: Online parametric timed pattern matching with automata-based skipping. CoRR abs/1903.07328 (2019). http://arxiv.org/abs/1903.07328

    Google Scholar 

  34. Waga, M., André, É., Hasuo, I.: Symbolic monitoring against specifications parametric in time and data. In: To appear in Proceedings of the CAV 2019

    Google Scholar 

  35. Waga, M., Hasuo, I., Suenaga, K.: Efficient online timed pattern matching by automata-based skipping. In: Abate, A., Geeraerts, G. (eds.) FORMATS 2017. LNCS, vol. 10419, pp. 224–243. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-65765-3_13

    Chapter  MATH  Google Scholar 

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Authors and Affiliations

  1. National Institute of Informatics, Tokyo, Japan

    Masaki Waga

  2. SOKENDAI (The Graduate University for Advanced Studies), Tokyo, Japan

    Masaki Waga

  3. JSPS Research Fellow, Tokyo, Japan

    Masaki Waga

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  1. Masaki Waga
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Correspondence to Masaki Waga .

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  1. Université Paris 13, Villetaneuse, France

    Étienne André

  2. University of Twente, Enschede, The Netherlands

    Mariëlle Stoelinga

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Waga, M. (2019). Online Quantitative Timed Pattern Matching with Semiring-Valued Weighted Automata. In: André, É., Stoelinga, M. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2019. Lecture Notes in Computer Science(), vol 11750. Springer, Cham. https://doi.org/10.1007/978-3-030-29662-9_1

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