Skip to main content
SpringerLink
Log in

Clairvoyant Monitoring for Signal Temporal Logic

  • Conference paper
  • First Online:
Formal Modeling and Analysis of Timed Systems (FORMATS 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12288))

Abstract

In this paper, we consider the problem of monitoring temporal patterns expressed in Signal Temporal Logic (STL) over time-series data in a clairvoyant fashion. Existing offline or online monitoring algorithms can only compute the satisfaction of a given STL formula on the time-series data that is available. We use off-the-shelf statistical time-series analysis techniques to fit available data to a model and use this model to forecast future signal values. We derive the joint probability distribution of predicted signal values and use this to compute the satisfaction probability of a given signal pattern over the prediction horizon. There are numerous potential applications of such prescient detection of temporal patterns. We demonstrate practicality of our approach on case studies in automated insulin delivery, unmanned aerial vehicles, and household power consumption data.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    We can easily extend clairvoyant monitoring of unbounded horizon STL formulas over entire traces by considering the notion of nominal robustness [10]. This would also require us to track the robustness over the signal prefix.

  2. 2.

    When signals are evaluated w.r.t. Signal Temporal Logic formulas, we assume that the signal is defined at each time point in the interval \([0,t_N]\). We can do this using piecewise constant interpolation, i.e. \(\forall i \in [0,N-1]: (t_i \le t < t_{i+1}) \implies x(t) = x(t_i)\).

  3. 3.

    Our implementation was done in Matlab, and Matlab has a certain precision when computing probabilities, and the number 1 is actually \(1 -\delta \), where \(\delta \) is smaller than the machine precision. This indicates that the probability is so high that it is practically 1.

References

  1. 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 

  2. Babaee, R., Gurfinkel, A., Fischmeister, S.: Predictive run-time verification of discrete-time reachability properties in black-box systems using trace-level abstraction and statistical learning. In: Colombo, C., Leucker, M. (eds.) RV 2018. LNCS, vol. 11237, pp. 187–204. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03769-7_11

    Chapter  Google Scholar 

  3. Babaee, R., Gurfinkel, A., Fischmeister, S.: \(\cal{P}revent\): a predictive run-time verification framework using statistical learning. In: Johnsen, E.B., Schaefer, I. (eds.) SEFM 2018. LNCS, vol. 10886, pp. 205–220. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-92970-5_13

    Chapter  Google Scholar 

  4. Bartocci, E., Bortolussi, L., Sanguinetti, G.: Learning temporal logical properties discriminating ECG models of cardiac arrhytmias. arXiv preprint arXiv:1312.7523 (2013)

  5. Bartocci, E., Bortolussi, L., Sanguinetti, G.: Data-driven statistical learning of temporal logic properties. In: Legay, A., Bozga, M. (eds.) FORMATS 2014. LNCS, vol. 8711, pp. 23–37. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-10512-3_3

    Chapter  MATH  Google Scholar 

  6. Bartocci, E., et al.: Specification-based monitoring of cyber-physical systems: a survey on theory, tools and applications. In: Bartocci, E., Falcone, Y. (eds.) Lectures on Runtime Verification. LNCS, vol. 10457, pp. 135–175. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-75632-5_5

    Chapter  Google Scholar 

  7. Bartocci, E., et al.: Adaptive runtime verification. In: Qadeer, S., Tasiran, S. (eds.) RV 2012. LNCS, vol. 7687, pp. 168–182. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-35632-2_18

    Chapter  Google Scholar 

  8. Brockwell, P.J., Davis, R.A., Calder, M.V.: Introduction to Time Series and Forecasting, vol. 2. Springer, Heidelberg (2002). https://doi.org/10.1007/b97391

    Book  MATH  Google Scholar 

  9. Cameron, F., Fainekos, G., Maahs, D.M., Sankaranarayanan, S.: Towards a verified artificial pancreas: challenges and solutions for runtime verification. In: Bartocci, E., Majumdar, R. (eds.) RV 2015. LNCS, vol. 9333, pp. 3–17. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-23820-3_1

    Chapter  Google Scholar 

  10. Deshmukh, J.V., Donzé, A., Ghosh, S., Jin, X., Juniwal, G., Seshia, S.A.: Robust online monitoring of signal temporal logic. Formal Meth. Syst. Des. 51(1), 5–30 (2017). https://doi.org/10.1007/s10703-017-0286-7

    Article  MATH  Google Scholar 

  11. Dua, D., Graff, C.: UCI machine learning repository (2017). http://archive.ics.uci.edu/ml

  12. Duggirala, P.S., Mitra, S., Viswanathan, M., Potok, M.: C2E2: a verification tool for stateflow models. In: Baier, C., Tinelli, C. (eds.) TACAS 2015. LNCS, vol. 9035, pp. 68–82. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46681-0_5

    Chapter  Google Scholar 

  13. Geist, J., Rozier, K.Y., Schumann, J.: Runtime observer pairs and Bayesian network reasoners on-board FPGAs: flight-certifiable system health management for embedded systems. In: Bonakdarpour, B., Smolka, S.A. (eds.) RV 2014. LNCS, vol. 8734, pp. 215–230. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-11164-3_18

    Chapter  Google Scholar 

  14. Ho, H.-M., Ouaknine, J., Worrell, J.: Online monitoring of metric temporal logic. In: Bonakdarpour, B., Smolka, S.A. (eds.) RV 2014. LNCS, vol. 8734, pp. 178–192. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-11164-3_15

    Chapter  Google Scholar 

  15. Hoxha, B., Abbas, H., Fainekos, G.: Benchmarks for temporal logic requirements for automotive systems. In: Frehse, G., Althoff, M. (eds.) ARCH14-15. 1st and 2nd International Workshop on Applied veRification for Continuous and Hybrid Systems. EPiC Series in Computing, vol. 34, pp. 25–30. EasyChair (2015)

    Google Scholar 

  16. Jin, X., Deshmukh, J.V., Kapinski, J., Ueda, K., Butts, K.: Powertrain control verification benchmark. In: Proceedings of the 17th International Conference on Hybrid Systems: Computation and Control, pp. 253–262. ACM (2014)

    Google Scholar 

  17. Kalajdzic, K., Bartocci, E., Smolka, S.A., Stoller, S.D., Grosu, R.: Runtime verification with particle filtering. In: Legay, A., Bensalem, S. (eds.) RV 2013. LNCS, vol. 8174, pp. 149–166. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40787-1_9

    Chapter  Google Scholar 

  18. Kapinski, J., et al.: ST-Lib: a library for specifying and classifying model behaviors. In: SAE Technical Paper. SAE (2016)

    Google Scholar 

  19. Kong, Z., Jones, A., Medina Ayala, A., Aydin Gol, E., Belta, C.: Temporal logic inference for classification and prediction from data. In: Proceedings of HSCC, pp. 273–282 (2014)

    Google Scholar 

  20. Moosbrugger, P., Rozier, K.Y., Schumann, J.: R2U2: monitoring and diagnosis of security threats for unmanned aerial systems. Formal Methods Syst. Des. 51(1), 31–61 (2017). https://doi.org/10.1007/s10703-017-0275-x

    Article  Google Scholar 

  21. Qin, X., Deshmukh, J.V.: Joint probability distribution of prediction errors of ARIMA. CoRR abs/1811.04685 (2018), http://arxiv.org/abs/1811.04685

  22. Roehm, H., Gmehlich, R., Heinz, T., Oehlerking, J., Woehrle, M.: Industrial examples of formal specifications for test case generation. In: Workshop on Applied veRification for Continuous and Hybrid Systems, ARCH. pp. 80–88 (2015)

    Google Scholar 

  23. Schumann, J., Moosbrugger, P., Rozier, K.Y.: R2U2: monitoring and diagnosis of security threats for unmanned aerial systems. In: Bartocci, E., Majumdar, R. (eds.) RV 2015. LNCS, vol. 9333, pp. 233–249. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-23820-3_15

    Chapter  Google Scholar 

  24. Schumann, J., Moosbrugger, P., Rozier, K.Y.: Runtime analysis with R2U2: a tool exhibition report. In: Falcone, Y., Sánchez, C. (eds.) RV 2016. LNCS, vol. 10012, pp. 504–509. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-46982-9_35

    Chapter  Google Scholar 

  25. Sistla, A.P., Žefran, M., Feng, Y.: Monitorability of stochastic dynamical systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 720–736. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22110-1_58

    Chapter  Google Scholar 

  26. Stoller, S.D., et al.: Runtime verification with state estimation. In: Khurshid, S., Sen, K. (eds.) RV 2011. LNCS, vol. 7186, pp. 193–207. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29860-8_15

    Chapter  Google Scholar 

  27. Zhang, X., Leucker, M., Dong, W.: Runtime verification with predictive semantics. In: Goodloe, A.E., Person, S. (eds.) NFM 2012. LNCS, vol. 7226, pp. 418–432. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-28891-3_37

    Chapter  Google Scholar 

Download references

Acknowledgments

We thank the anonymous reviewers for their careful reading of the paper and the constructive feedback. We gratefully acknowledge the support by the National Science Foundation under grant no. CCF/SHF-1910088, and a grant from Toyota Motors R&D North America. We thank Yue Wu and Weixin Cai for fruitful discussions that helped shape the proofs for Theorem 1.

Author information

Authors and Affiliations

  1. University of Southern California, Los Angeles, USA

    Xin Qin & Jyotirmoy V. Deshmukh

Authors
  1. Xin Qin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jyotirmoy V. Deshmukh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Xin Qin or Jyotirmoy V. Deshmukh .

Editor information

Editors and Affiliations

  1. Inria, Université de Rennes, Rennes, France

    Nathalie Bertrand

  2. Radboud University, Nijmegen, The Netherlands

    Nils Jansen

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Qin, X., Deshmukh, J.V. (2020). Clairvoyant Monitoring for Signal Temporal Logic. In: Bertrand, N., Jansen, N. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2020. Lecture Notes in Computer Science(), vol 12288. Springer, Cham. https://doi.org/10.1007/978-3-030-57628-8_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-57628-8_11

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-57627-1

  • Online ISBN: 978-3-030-57628-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation