Almost Event-Rate Independent Monitoring of Metric Dynamic Logic

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10548)


Linear temporal logic (LTL) and its quantitative extension metric temporal logic (MTL) are standard languages for specifying system behaviors. Regular expressions are an even more expressive formalism in the non-metric setting and several extensions of LTL, including the recently proposed linear dynamic logic (LDL), offer regular-expression-like constructs. We extend LDL with past operators and quantitative features. The resulting metric dynamic logic (MDL) offers the quantitative temporal conveniences of MTL while increasing its expressiveness. We develop and evaluate an online monitoring algorithm for MDL whose space-consumption is almost event-rate independent—a notion that characterizes monitors that scale to high-velocity event streams.



Felix Klaedtke pointed us to a motivating example of a property not expressible in MTL. Bhargav Bhatt, Domenico Bianculli, and three anonymous reviewers provided helpful feedback on earlier drafts of this paper. Srđan Krstić is supported by the Swiss National Science Foundation grant Big Data Monitoring (167162). The authors are listed alphabetically.


  1. 1.
    Aerial: An almost event-rate independent monitor for metric temporal logic (2017).
  2. 2.
    QCheck: QuickCheck inspired property-based testing for OCaml (2017).
  3. 3.
    Antimirov, V.: Partial derivatives of regular expressions and finite automaton constructions. Theor. Comput. Sci. 155(2), 291–319 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Asarin, E., Caspi, P., Maler, O.: Timed regular expressions. J. ACM 49(2), 172–206 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Basin, D.A., 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). doi: 10.1007/978-3-662-54580-5_6 CrossRefGoogle Scholar
  6. 6.
    Basin, D.A., Klaedtke, F., Müller, S., Pfitzmann, B.: Runtime monitoring of metric first-order temporal properties. In: Hariharan, R., Mukund, M., Vinay, V. (eds.) FSTTCS 2008. LIPIcs, vol. 2, pp. 49–60. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2008)Google Scholar
  7. 7.
    Basin, D.A., Klaedtke, F., Müller, S., Zălinescu, E.: Monitoring metric first-order temporal properties. J. ACM 62(2), 1–45 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Basin, D.A., Klaedtke, F., Zălinescu, E.: Algorithms for monitoring real-time properties. In: Khurshid, S., Sen, K. (eds.) RV 2011. LNCS, vol. 7186, pp. 260–275. Springer, Heidelberg (2012). doi: 10.1007/978-3-642-29860-8_20 CrossRefGoogle Scholar
  9. 9.
    Bouyer, P., Chevalier, F., Markey, N.: On the expressiveness of TPTL and MTL. Inf. Comput. 208(2), 97–116 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Brzozowski, J.A.: Derivatives of regular expressions. J. ACM 11(4), 481–494 (1964)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Dax, C., Klaedtke, F., Lange, M.: On regular temporal logics with past. Acta Inf. 47(4), 251–277 (2010)CrossRefzbMATHGoogle Scholar
  12. 12.
    De Giacomo, G., De Masellis, R., Grasso, M., Maggi, F.M., Montali, M.: LTLf and LDLf monitoring: A technical report. CoRR abs/1405.0054 (2014)Google Scholar
  13. 13.
    De Giacomo, G., De Masellis, R., Grasso, M., Maggi, F.M., Montali, M.: Monitoring business metaconstraints based on LTL and LDL for finite traces. In: Sadiq, S., Soffer, P., Völzer, H. (eds.) BPM 2014. LNCS, vol. 8659, pp. 1–17. Springer, Cham (2014). doi: 10.1007/978-3-319-10172-9_1 Google Scholar
  14. 14.
    De Giacomo, G., Vardi, M.Y.: Linear temporal logic and linear dynamic logic on finite traces. In: Rossi, F. (ed.) IJCAI-13, pp. 854–860. AAAI Press (2013)Google Scholar
  15. 15.
    Faymonville, P., Zimmermann, M.: Parametric linear dynamic logic. In: Peron, A., Piazza, C. (eds.) Proceedings 5th GandALF 2014, EPTCS, vol. 161, pp. 60–73 (2014)Google Scholar
  16. 16.
    Faymonville, P., Zimmermann, M.: Parametric linear dynamic logic. Inf. Comput. 253, 237–256 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Fischer, M.J., Ladner, R.E.: Propositional dynamic logic of regular programs. J. Comput. Syst. Sci. 18(2), 194–211 (1979)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    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). doi: 10.1007/3-540-46002-0_24 CrossRefGoogle Scholar
  19. 19.
    Henriksen, J.G., Thiagarajan, P.: Dynamic linear time temporal logic. Ann. Pure Appl. Logic 96(1), 187–207 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Kapoutsis, C.: Removing bidirectionality from nondeterministic finite automata. In: Jȩdrzejowicz, J., Szepietowski, A. (eds.) MFCS 2005. LNCS, vol. 3618, pp. 544–555. Springer, Heidelberg (2005). doi: 10.1007/11549345_47 CrossRefGoogle Scholar
  21. 21.
    Koymans, R.: Specifying real-time properties with metric temporal logic. Real-Time Syst. 2(4), 255–299 (1990)CrossRefGoogle Scholar
  22. 22.
    Leucker, M., Sánchez, C.: Regular linear temporal logic. In: Jones, C.B., Liu, Z., Woodcock, J. (eds.) ICTAC 2007. LNCS, vol. 4711, pp. 291–305. Springer, Heidelberg (2007). doi: 10.1007/978-3-540-75292-9_20 CrossRefGoogle Scholar
  23. 23.
    Sánchez, C., Leucker, M.: Regular linear temporal logic with past. In: Barthe, G., Hermenegildo, M. (eds.) VMCAI 2010. LNCS, vol. 5944, pp. 295–311. Springer, Heidelberg (2010). doi: 10.1007/978-3-642-11319-2_22 CrossRefGoogle Scholar
  24. 24.
    Tange, O.: GNU parallel - the command-line power tool.;login: USENIX Mag. 36(1), 42–47 (2011). Google Scholar
  25. 25.
    Thati, P., Roşu, G.: Monitoring algorithms for metric temporal logic specifications. Electr. Notes Theor. Comput. Sci. 113, 145–162 (2005)CrossRefGoogle Scholar
  26. 26.
    Ulus, D.: Montre: A tool for monitoring timed regular expressions. arXiv preprint (2016). arXiv:1605.05963
  27. 27.
    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). doi: 10.1007/978-3-319-10512-3_16 Google Scholar
  28. 28.
    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). doi: 10.1007/978-3-662-49674-9_47 CrossRefGoogle Scholar
  29. 29.
    Vardi, M.Y.: From Church and Prior to PSL. In: Grumberg, O., Veith, H. (eds.) 25 Years of Model Checking. LNCS, vol. 5000, pp. 150–171. Springer, Heidelberg (2008). doi: 10.1007/978-3-540-69850-0_10 CrossRefGoogle Scholar
  30. 30.
    Wolper, P.: Temporal logic can be more expressive. Inform. Control 56(1/2), 72–99 (1983)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

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

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