Skip to main content
SpringerLink
Log in

Property-Directed Verified Monitoring of Signal Temporal Logic

  • Conference paper
  • First Online:
Runtime Verification (RV 2020)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 12399))

Included in the following conference series:

Abstract

Signal Temporal Logic monitoring over numerical simulation traces has emerged as an effective approach to approximate verification of continuous and hybrid systems. In this paper we explore an exact verification procedure for STL properties based on monitoring verified traces in the form of Taylor model flowpipes as produced by the Flow* verified integrator. We explore how tight integration with Flow*’s symbolic flowpipe representation can lead to more precise and more efficient monitoring. We then show how the performance of monitoring can be increased substantially by introducing masks, a property-directed refinement of our method which restricts flowpipe monitoring to the time regions relevant to the overall truth of a complex proposition. Finally, we apply our implementation of these methods to verifying properties of a challenging continuous system, evaluating the impact of each aspect of our procedure on monitoring performance.

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.

    https://github.com/twright/Logic-of-Behaviour-in-Uncertain-Contexts.

References

  1. Althoff, M.: An Introduction to CORA 2015. In: Proceedings of the Workshop on Applied Verification for Continuous and Hybrid Systems (2015)

    Google Scholar 

  2. Alur, R., Henzinger, T.A., Ho, P.-H.: Automatic symbolic verification of embedded systems. IEEE Trans. Softw. Eng. 22(3), 181–201 (1996)

    Article  Google Scholar 

  3. 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 

  4. Bae, K., Lee, J.: Bounded model checking of signal temporal logic properties using syntactic separation. Proc. ACM Program. Lang. 3(POPL), 51 (2019)

    Article  Google Scholar 

  5. Banks, C.J., and Stark, I.: A more sensitive context. arXiv:1702.03288 (2017)

  6. Behnel, S., Bradshaw, R., Citro, C., Dalcin, L., Seljebotn, D., Smith, K.: Cython: the best of both worlds. Comput. Sci. Eng. 13(2), 31–39 (2011)

    Article  Google Scholar 

  7. Berz, M., Hoefkens, J.: Verified high-order inversion of functional depedencies and interval newton methods. Reliable Comput. 7(5), 379–398 (2001)

    Article  MathSciNet  Google Scholar 

  8. Berz, M., Hoffstätter, G.: Computation and application of Taylor polynomials with interval remainder bounds. Reliable Comput. 4(1), 83–97 (1998)

    Article  MathSciNet  Google Scholar 

  9. Berz, M., Makino, K.: Verified integration of ODEs and flows using differential algebraic methods on high-order Taylor models. Reliable Comput. 4(4), 361–369 (1998)

    Article  MathSciNet  Google Scholar 

  10. Bresolin, D.: HyLTL: a temporal logic for model checking hybrid systems. Electron. Proc. Theoret. Comput. Sci. 124, 73–84 (2013)

    Article  MathSciNet  Google Scholar 

  11. Bruns, G., Godefroid, P.: Model checking partial state spaces with 3-valued temporal logics. In: Halbwachs, N., Peled, D. (eds.) CAV 1999. LNCS, vol. 1633, pp. 274–287. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48683-6_25

    Chapter  Google Scholar 

  12. Chen, X.: Reachability analysis of non-linear hybrid systems using taylor models. Ph.D thesis, Fachgruppe Informatik, RWTH Aachen University (2015)

    Google Scholar 

  13. Chen, X., Ábrahám, E., Sankaranarayanan, S.: Flow*: an analyzer for non-linear hybrid systems. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 258–263. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-39799-8_18

    Chapter  Google Scholar 

  14. Chen, X., Sankaranarayanan, S.: Decomposed reachability analysis for nonlinear systems. In: 2016 IEEE Real-Time Systems Symposium (RTSS), pp. 13–24 (2016)

    Google Scholar 

  15. Chen, X., Schupp, S., Makhlouf, I.B., Ábrahám, E., Frehse, G., Kowalewski, S.: A benchmark suite for hybrid systems reachability analysis. In: Havelund, K., Holzmann, G., Joshi, R. (eds.) NFM 2015. LNCS, vol. 9058, pp. 408–414. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-17524-9_29

    Chapter  Google Scholar 

  16. Cimatti, A., Griggio, A., Mover, S., Tonetta, S.: Verifying LTL properties of hybrid systems with K-Liveness. In: Biere, A., Bloem, R. (eds.) CAV 2014. LNCS, vol. 8559, pp. 424–440. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-08867-9_28

    Chapter  Google Scholar 

  17. de Moura, L., Bjørner, N.: Z3: an efficient SMT solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78800-3_24

    Chapter  Google Scholar 

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

    Article  MATH  Google Scholar 

  19. 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 

  20. 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 

  21. Fages, F., Rizk, A.: On temporal logic constraint solving for analyzing numerical data time series. Theoret. Comput. Sci. 408(1), 55–65 (2008)

    Article  MathSciNet  Google Scholar 

  22. Fainekos, G.E., Pappas, G.J.: Robust sampling for MITL specifications. In: Raskin, J.-F., Thiagarajan, P.S. (eds.) FORMATS 2007. LNCS, vol. 4763, pp. 147–162. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-75454-1_12

    Chapter  Google Scholar 

  23. Fisman, D., Kugler, H.: Temporal reasoning on incomplete paths. In: Margaria, T., Steffen, B. (eds.) ISoLA 2018. LNCS, vol. 11245, pp. 28–52. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03421-4_3

    Chapter  Google Scholar 

  24. Gao, S., Kong, S., Clarke, E.M.: dReal: an SMT solver for nonlinear theories over the reals. In: Bonacina, M.P. (ed.) CADE 2013. LNCS (LNAI), vol. 7898, pp. 208–214. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38574-2_14

    Chapter  Google Scholar 

  25. Ishii, D., Goldsztejn, A.: HySIA: tool for simulating and monitoring hybrid automata based on interval analysis. In: Lahiri, S., Reger, G. (eds.) RV 2017. LNCS, vol. 10548, pp. 370–379. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-67531-2_23

    Chapter  Google Scholar 

  26. Ishii, D., Yonezaki, N., Goldsztejn, A.: Monitoring bounded LTL properties using interval analysis. Electron. Notes Theoret. Comput. Sci. 317, 85–100 (2015)

    Article  MathSciNet  Google Scholar 

  27. Ishii, D., Yonezaki, N., Goldsztejn, A.: Monitoring temporal properties using interval analysis. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. 99(2), 442–453 (2016)

    Article  Google Scholar 

  28. Jeannin, J.-B., Platzer, A.: dTL\(^2\): differential temporal dynamic logic with nested temporalities for hybrid systems. In: Demri, S., Kapur, D., Weidenbach, C. (eds.) IJCAR 2014. LNCS (LNAI), vol. 8562, pp. 292–306. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-08587-6_22

    Chapter  Google Scholar 

  29. Kolmogorov, A.N., Fomin, S.V.: Introductory Real Analysis. Courier Corporation, Chelmsford (1975)

    Google Scholar 

  30. Kong, S., Gao, S., Chen, W., Clarke, E.: dReach: \(\delta \)-reachability analysis for hybrid systems. In: Baier, C., Tinelli, C. (eds.) TACAS 2015. LNCS, vol. 9035, pp. 200–205. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46681-0_15

    Chapter  Google Scholar 

  31. Liu, J., Zhan, N., Zhao, H., Zou, L.: Abstraction of elementary hybrid systems by variable transformation. In: Bjørner, N., de Boer, F. (eds.) FM 2015. LNCS, vol. 9109, pp. 360–377. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-19249-9_23

    Chapter  Google Scholar 

  32. Luisa Vissat, L., Hillston, J., Loreti, M., Nenzi, L.: Automatic verification of reliability requirements of spatio-temporal analysis using three-valued spatio-temporal logic. In: Proceedings of the 11th EAI International Conference on Performance Evaluation Methodologies and Tools, pp. 225–226. ACM (2017)

    Google Scholar 

  33. Makino, K., Berz, M.: Efficient control of the dependency problem based on taylor model methods. Reliable Comput. 5(1), 3–12 (1999)

    Article  MathSciNet  Google Scholar 

  34. Makino, K., Berz, M.: Suppression of the wrapping effect by Taylor model-based verified integrators: Long-term stabilization by preconditioning. Int. J. Diff. Equ. Appl. 10(4), 385–403 (2011)

    MathSciNet  MATH  Google Scholar 

  35. 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 

  36. Maler, O., Nickovic, D., Pnueli, A.: Checking temporal properties of discrete, timed and continuous behaviors. In: Avron, A., Dershowitz, N., Rabinovich, A. (eds.) Pillars of Computer Science. LNCS, vol. 4800, pp. 475–505. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78127-1_26

    Chapter  MATH  Google Scholar 

  37. Moore, R.E., Kearfott, R.B., Cloud, M.J.: Introduction to Interval Analysis. Siam, Philadelphia (2009)

    Book  Google Scholar 

  38. Nickovic, D., Maler, O.: AMT: a property-based monitoring tool for analog systems. In: Raskin, J.-F., Thiagarajan, P.S. (eds.) FORMATS 2007. LNCS, vol. 4763, pp. 304–319. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-75454-1_22

    Chapter  Google Scholar 

  39. Peña, J.M., Sauer, T.: On the multivariate horner scheme. SIAM J. Numer. Anal. 37(4), 1186–1197 (2000)

    Article  MathSciNet  Google Scholar 

  40. Piazza, C., Antoniotti, M., Mysore, V., Policriti, A., Winkler, F., Mishra, B.: Algorithmic algebraic model checking I: challenges from systems biology. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 5–19. Springer, Heidelberg (2005). https://doi.org/10.1007/11513988_3

    Chapter  Google Scholar 

  41. Roehm, H., Oehlerking, J., Heinz, T., Althoff, M.: STL model checking of continuous and hybrid systems. In: Artho, C., Legay, A., Peled, D. (eds.) ATVA 2016. LNCS, vol. 9938, pp. 412–427. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-46520-3_26

    Chapter  MATH  Google Scholar 

  42. Vardi, M.Y., Wolper, P.: An automata-theoretic approach to automatic program verification. In: Proceedings of the First Symposium on Logic in Computer Science, pp. 322–331 (1986)

    Google Scholar 

  43. Vilar, J.M.G., Kueh, H.Y., Barkai, N., Leibler, S.: Mechanisms of noise resistance in genetic oscillators. Proc. Nat. Acad. Sci. 99(9), 5988–5992 (2002)

    Article  Google Scholar 

  44. Wright, T., Stark, I.: Technical report: property-directed verified monitoring of signal temporal logic. arXiv:2008.06589 (2020)

Download references

Acknowledgements

We would like to thank Paul Jackson for many useful discussions of Taylor models and Flow*, Chris Banks for providing feedback on our approach, Kristjan Liiva for useful discussions of Flow*’s code and for his patches to Flow* for native floating point arithmetic, and Jos Gibbons and Juliet Cooke for providing feedback on drafts of this report. Thanks also go to our anonymous reviewers for helpful feedback, and for pointing out the connections of our work to  [18].

This work was supported by the Engineering and Physical Sciences Research Council (grant EP/L01503X/1), EPSRC Centre for Doctoral Training in Pervasive Parallelism at the University of Edinburgh, School of Informatics.

Author information

Authors and Affiliations

  1. School of Informatics, University of Edinburgh, Edinburgh, UK

    Thomas Wright & Ian Stark

Authors
  1. Thomas Wright
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ian Stark
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Thomas Wright .

Editor information

Editors and Affiliations

  1. University of Southern California, Los Angeles, CA, USA

    Jyotirmoy Deshmukh

  2. AIT Austrian Institute of Technology GmbH, Vienna, Austria

    Dejan Ničković

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

Wright, T., Stark, I. (2020). Property-Directed Verified Monitoring of Signal Temporal Logic. In: Deshmukh, J., Ničković, D. (eds) Runtime Verification. RV 2020. Lecture Notes in Computer Science(), vol 12399. Springer, Cham. https://doi.org/10.1007/978-3-030-60508-7_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-60508-7_19

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-60507-0

  • Online ISBN: 978-3-030-60508-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation