Multi-head Monitoring of Metric Temporal Logic

  • Martin RaszykEmail author
  • David Basin
  • Srđan Krstić
  • Dmitriy TraytelEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11781)


We present a novel approach to the offline monitoring of specifications expressed in metric temporal logic (MTL). Our monitoring algorithm exploits multiple one-way reading heads that traverse a trace sequentially. We present both theoretical and practical results that show this substantially improves upon the state-of-the-art. In particular, our algorithm is the first offline monitoring algorithm for MTL with past and bounded-future temporal operators that is almost trace-length independent and outputs a trace of Boolean verdicts denoting the monitored formula’s satisfaction at every position in the input trace. In addition, our algorithm’s worst-case space complexity is linear in the formula size, while previous algorithms were exponential. Moreover, we compare our implementation of the algorithm with another almost trace-length independent tool that outputs non-standard verdicts to achieve this space complexity. Our tool used less memory and runs significantly faster, for example yielding a 10-fold improvement on average on random formulas, while producing better output.



We thank the anonymous reviewers for their valuable suggestions on earlier drafts of this paper, which helped us to improve the presentation. This research is supported by the Swiss National Science Foundation grant “Big Data Monitoring” (167162).


  1. 1.
    Asarin, E., Caspi, P., Maler, O.: Timed regular expressions. J. ACM 49(2), 172–206 (2002)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Basin, D., Bhatt, B.N., Krstić, S., Traytel, D.: Almost event-rate independent monitoring. Formal Methods Syst. Des. 1–30 (2019). Scholar
  3. 3.
    Basin, D., Bhatt, B.N., Traytel, D.: Almost event-rate independent monitoring of metric temporal logic. In: Legay, A., Margaria, T. (eds.) TACAS 2017. LNCS, vol. 10206, pp. 94–112. Springer, Heidelberg (2017). Scholar
  4. 4.
    Basin, D., Klaedtke, F., Müller, S., Zălinescu, E.: Monitoring metric first-order temporal properties. J. ACM 62(2), 15 (2015)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Basin, D., Klaedtke, F., Zălinescu, E.: The MonPoly monitoring tool. In: Reger, G., Havelund, K. (eds.) RV-CuBES 2017. Kalpa Publications in Computing, vol. 3, pp. 19–28. EasyChair (2017)Google Scholar
  6. 6.
    Basin, D., Klaedtke, F., Zălinescu, E.: Algorithms for monitoring real-time properties. Acta Inf. 55(4), 309–338 (2018)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Basin, D., Krstić, S., Traytel, D.: AERIAL: almost event-rate independent algorithms for monitoring metric regular properties. In: Reger, G., Havelund, K. (eds.) RV-CuBES 2017. Kalpa Publications in Computing, vol. 3, pp. 29–36. EasyChair (2017)Google Scholar
  8. 8.
    Bauer, A., Leucker, M., Schallhart, C.: Runtime verification for LTL and TLTL. ACM Trans. Softw. Eng. Methodol. 20(4), 14:1–14:64 (2011)CrossRefGoogle Scholar
  9. 9.
    Convent, L., Hungerecker, S., Leucker, M., Scheffel, T., Schmitz, M., Thoma, D.: TeSSLa: temporal stream-based specification language. In: Massoni, T., Mousavi, M.R. (eds.) SBMF 2018. LNCS, vol. 11254, pp. 144–162. Springer, Cham (2018). Scholar
  10. 10.
    D’Angelo, B., et al.: LOLA: runtime monitoring of synchronous systems. In: TIME 2005, pp. 166–174. IEEE Computer Society (2005)Google Scholar
  11. 11.
    Falcone, Y., Krstić, S., Reger, G., Traytel, D.: A taxonomy for classifying runtime verification tools. In: Colombo, C., Leucker, M. (eds.) RV 2018. LNCS, vol. 11237, pp. 241–262. Springer, Cham (2018). Scholar
  12. 12.
    Faymonville, P., Finkbeiner, B., Schwenger, M., Torfah, H.: Real-time stream-based monitoring. CoRR abs/1711.03829 (2017)Google Scholar
  13. 13.
    Finkbeiner, B., Sipma, H.: Checking finite traces using alternating automata. Formal Methods Syst. Des. 24(2), 101–127 (2004)CrossRefGoogle Scholar
  14. 14.
    Gorostiaga, F., Sánchez, C.: Striver: stream runtime verification for real-time event-streams. In: Colombo, C., Leucker, M. (eds.) RV 2018. LNCS, vol. 11237, pp. 282–298. Springer, Cham (2018). Scholar
  15. 15.
    Gray, J., Shenoy, P.J.: Rules of thumb in data engineering. In: Lomet, D.B., Weikum, G. (eds.) ICDE 2000, pp. 3–10. IEEE Computer Society (2000)Google Scholar
  16. 16.
    Havelund, K., Roşu, G.: Synthesizing monitors for safety properties. In: Katoen, J.-P., Stevens, P. (eds.) TACAS 2002. LNCS, vol. 2280, pp. 342–356. Springer, Heidelberg (2002). Scholar
  17. 17.
    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). Scholar
  18. 18.
    Ibarra, O.H.: A note on semilinear sets and bounded-reversal multihead pushdown automata. Inf. Process. Lett. 3(1), 25–28 (1974)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Koymans, R.: Specifying real-time properties with metric temporal logic. Real-Time Syst. 2(4), 255–299 (1990)CrossRefGoogle Scholar
  20. 20.
    Raszyk, M., Basin, D., Krstić, S., Traytel, D.: HYDRA. (2019)
  21. 21.
    Raszyk, M., Basin, D., Traytel, D.: From nondeterministic to multi-head deterministic finite-state transducers. In: Baier, C., Chatzigiannakis, I., Flocchini, P., Leonardi, S. (eds.) ICALP 2019, LIPIcs, vol. 132, pp. 127:1–127:14. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik (2019)Google Scholar
  22. 22.
    Roşu, G., Havelund, K.: Rewriting-based techniques for runtime verification. Autom. Softw. Eng. 12(2), 151–197 (2005)CrossRefGoogle Scholar
  23. 23.
    Sánchez, C.: Online and offline stream runtime verification of synchronous systems. In: Colombo, C., Leucker, M. (eds.) RV 2018. LNCS, vol. 11237, pp. 138–163. Springer, Cham (2018). Scholar
  24. 24.
    Thati, P., Roşu, G.: Monitoring algorithms for metric temporal logic specifications. Electr. Notes Theor. Comput. Sci. 113, 145–162 (2005)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of Information Security, Department of Computer ScienceETH ZürichZurichSwitzerland

Personalised recommendations