Skip to main content
SpringerLink
Log in

An extension of first-order LTL with rules with application to runtime verification

  • General
  • Special Issue: RV 2019
  • Published:
International Journal on Software Tools for Technology Transfer Aims and scope Submit manuscript

Abstract

Linear temporal logic (LTL) is extensively used in formal methods, in particular in runtime verification (RV) and in model checking. Its propositional version was shown by Wolper (1983, Inform Control 56(1/2): 72–99) to be limited in expressiveness. Several extensions of propositional LTL, which promote the expressive power to that of Büchi automata, have therefore been proposed; however, none of those, by and large, have been adopted for formal methods. We present an extension of propositional LTL with rules, that is as expressive as these aforementioned extensions. We then show a similar deficiency in the expressiveness of first-order LTL and present an extension of it with rules, which parallels the propositional version. In our work on runtime verification, we focus on execution traces which consist of events that carry data, where a first-order version of LTL is needed, and in particular on past time versions of first-order LTL. In the previous work, we provided an algorithm for past time first-order LTL that uses BDDs to represent relations over data elements, and implemented it as a tool called DejaVu. In this paper, we propose a monitoring algorithm for the extension of past time first-order LTL with rules. This is implemented as an extension of DejaVu, and experimental results are provided.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Notes

  1. The logics are called monadic since they allow relations with one parameter that explicitly represents the time; hence, instead of occurrences of a proposition p in the temporal logic formulas, the monadic logics have a relation p where p(i) stands for p holds at time i. First-order monadic logic allows quantifying over the time variables, while second-order logic allows quantifying over the relations.

  2. For a counter-free language, there is an integer n such that for all words x, y, z and integers \(m \ge n\) we have that \(xy^m z \in L\) if and only if \(xy^n z \in L\).

  3. Finite domains are handled with some minor changes, see [24].

  4. This theory is based on the compactness theory of first-order logic, see [17] Chap. 4.

  5. Again, the definition can be extended to any number of variables.

  6. Other enumeration generation schemes are possible. Our implementation allows a garbage collection mechanism that can reuse enumerations that are no longer needed.

  7. With k bits, we can store \(2^k\) enumerations. It is possible to extend the number of bits used on the fly.

  8. An additional 900+ lines of mostly property-independent boilerplate code is generated.

References

  1. Alpern, B., Schneider, F.B.: Recognizing safety and liveness. Distrib. Comput. 2(3), 117–126 (1987)

    Article  Google Scholar 

  2. Attard, D.P., Cassar, I., Francalanza, A., Aceto, L., Ingólfsdóttir, A.: A runtime monitoring tool for actor-based systems. In: Gay, S., Ravara, A. (eds) Behavioural Types: from Theory to Tools, Chapter 3, pp. 49–76, River Publishers, Denmark (2017)

  3. Barringer, H., Goldberg, A., Havelund, K., Sen, K.: Rule-based runtime verification, Verification, Model Checking, and Abstract Interpretation (VMCAI’04), LNCS, vol. 44–57. Springer, Berlin (2004)

  4. Barringer, H., Rydeheard, D., Havelund, K.: Rule systems for run-time monitoring: from Eagle to RuleR. J. Log. Comput. (JLC), Vol. 20, No. 3. Oxford University Press, Oxford, pp. 675–706 (2008)

  5. Bartocci, E., Falcone, Y., Francalanza, A., Leucker, M., Reger, G.: An introduction to runtime verification, lectures on runtime verification - introductory and advanced topics, LNCS, vol. 1–23. Springer, Berlin (2018)

  6. Basin, D.A., Klaedtke, F., Marinovic, S., Zalinescu, En: Monitoring of temporal first-order properties with aggregations. Form. Meth. Syst. Des. 46(3), 262–285 (2015)

    Article  Google Scholar 

  7. Basin, D.A., Klaedtke, F., Müller, S., Zalinescu, E.: Monitoring metric first-order temporal properties. J. ACM 62(2), 1–45 (2015)

    Article  MathSciNet  Google Scholar 

  8. Bauer, A., Leucker, M., Schallhart, C.: The good, the bad, and the ugly, but how ugly is ugly?, Workshop on Runtime Verification (RV’07), LNCS, vol. 126–138. Springer, Berlin (2007)

  9. Bohn, J., Damm, W., Grumberg, O., Hungar, H., Laster, K.: First-order CTL model checking, International Conference on Foundations of Software Technology and Theoretical Computer Science, (FSTTCS’98), LNCS, vol. 283–294. Springer, Berlin (1998)

  10. Bryant, R.E.: Symbolic Boolean manipulation with ordered binary-decision diagrams. ACM Comput. Surv. 24(3), 293–318 (1992)

    Article  Google Scholar 

  11. Burch, J.R., Clarke, E.M., McMillan, K.L., Dill, D.L., Hwang, L.J.: Symbolic model checking: \(10^{20}\) states and beyond. Inform. Comput. 98(2), 142–170 (1992)

    Article  MathSciNet  Google Scholar 

  12. Chomicki, J.: Efficient checking of temporal integrity constraints using bounded history encoding. ACM Trans. Database Syst. 20(2), 149–186 (1995)

    Article  Google Scholar 

  13. Clarke, E.M., Grumberg, O., Peled, D.: Model checking. MIT Press, Chambridge (2000)

    MATH  Google Scholar 

  14. D’Angelo, B., Sankaranarayanan, S., Sánchez, C., Robinson, W., Finkbeiner, B., Sipma, H.B., Mehrotra, S., Manna, Z. LOLA: Runtime monitoring of synchronous systems, International Symposium on Temporal Representation and Reasoning (TIME’05), IEEE, 166-174. (2005)

  15. Decker, N., Leucker, M., Thoma, D.: Monitoring modulo theories. J. Softw. Tools Technol. Transf. 18(2), 205–225 (2016)

    Article  Google Scholar 

  16. DejaVu, https://github.com/havelund/dejavu

  17. Ebbinghaus, H.-D., Flum, J., Thomas, W.: Mathematical Logic. Undergraduate texts in mathematics. Springer, Berlin (1984)

    MATH  Google Scholar 

  18. Falcone, Y., Fernandez, J.-C., Mounier, L.: What can you verify and enforce at runtime? STTT 14(3), 349–382 (2012)

    Article  Google Scholar 

  19. Forgy, C.: Rete: A Fast algorithm for the many pattern/many object pattern match problem. Artif. Intell. 19, 17–37 (1982)

    Article  Google Scholar 

  20. Frenkel, H., Grumberg, O., Sheinvald, S.: An automata-theoretic approach to modeling systems and specifications over infinite data, NASA Formal Methods (NFM 17), LNCS, vol. 1–18. Springer, Berlin (2017)

  21. 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, International Conference on Runtime Verification (RV’14), LNCS, vol. 215–230. Springer, Berlin (2014)

  22. Gerth, R., Peled, D.A., Vardi, M.Y., Wolper, P.: Simple on-the-fly automatic verification of linear temporal logic. PSTV 3–18 (1995)

  23. Hallé, S., Villemaire, R.: Runtime enforcement of web service message contracts with data. IEEE Trans. Serv. Comput. 5(2), 192 (2012)

    Article  Google Scholar 

  24. Havelund, K., Peled, D.A., Ulus, D.: First-order temporal logic monitoring with BDDs, Formal Methods in Computer Aided Design (FMCAD’17), IEEE, pp. 116–123 (2017)

  25. Havelund, K., Peled, D.: Efficient runtime verification of first-order temporal properties. International Symposium on Model Checking Software (SPIN’18), LNCS Volume 10869, Springer, Berlin, pp. 26–47 (2018)

  26. Havelund, K., Reger, G., Thoma, D., Zălinescu, E.: Monitoring events that carry data, Lectures on Runtime Verification—Introductory and Advanced Topics, LNCS, vol. 61–102. Springer, Berlin (2018)

  27. Havelund, K., Rosu, G.: Synthesizing monitors for safety properties, Tools and Algorithms for the Construction and Analysis of Systems (TACAS 02), LNCS, vol. 342–356. Springer, Berlin (2002)

  28. Havelund, K.: Data automata in Scala, Theoretical Aspects of Software Engineering (TASE’14), IEEE Computer Society, pp. 1–9 (2014)

  29. Havelund, K.: Rule-based runtime verification revisited. Softw. Tools Technol. Transf. 17(2), 143–170 (2015)

    Article  Google Scholar 

  30. Havelund, K., Peled, D.A., Ulus, D.: First-order temporal logic monitoring with BDDs. Form. Meth. Syst. Des. 56, 1–21 (2019)

    Article  Google Scholar 

  31. Hella, L., Libkin, L., Nurmonen, J., Wong, L.: Logics with aggregate operators. J. ACM 48(4), 880–907 (2001)

    Article  MathSciNet  Google Scholar 

  32. IEEE Standard for Property Specification Language (PSL), Annex B. IEEE Std 1850TM-2010, (2010)

  33. JavaBDD, http://javabdd.sourceforge.net

  34. Kupferman, O., Vardi, M.Y.: Model checking of safety properties. Form. Methods Syst. Des. 19(3), 291–314 (2001)

    Article  Google Scholar 

  35. Maler, O., Nic̆ković, D.: Monitoring properties of analog and mixed-signal circuits. Int. J. Softw. Tools Technol. Transf., Springer, Berlin, vol. 15, pp. 247–268, (2013)

  36. Manna, Z., Pnueli, A.: The Temporal Logic of Reactive and Concurrent Systems—Specification. Springer, Berlin (1992)

    Book  Google Scholar 

  37. Mars Science Laboratory (MSL) mission website. http://mars.jpl.nasa.gov/msl

  38. Meredith, P.O., Jin, D., Griffith, D., Chen, F., Rosu, G.: An overview of the MOP runtime verification framework. Int. J. Softw. Tools Technol. Transf. vol. 14, pp. 249–289. Springer, Berlin (2012)

  39. Pike, L., Wegmann, N., Niller, S., Goodloe, A.: Copilot: Monitoring embedded systems. Innov. Syst. Softw. Eng. 9(4), 235–255 (2013)

    Article  Google Scholar 

  40. Reger, G., Cruz, H., Rydeheard, D.: MarQ: Monitoring at runtime with QEA, Tools and Algorithms for the Construction and Analysis of Systems (TACAS’15), LNCS, vol. 596–610. Springer, Berlin (2015)

  41. Schneider, J., Basin, D., Krstić, S., Traytel, D.: A formally verified monitor for metric first-order temporal logic, International Conference on Runtime Verification (RV’19), LNCS, vol. 310–328. Springer, Berlin (2019)

  42. Shafiei, N., Havelund, K., Mehlitz, P.C.: Actor-based runtime verification with MESA, International Conference on Runtime Verification (RV’20), LNCS, vol. 221–240. Springer, Berlin (2020)

  43. Sistla, A.P.: Theoretical Issues in the Design and Analysis of Distributed Systems, Ph.D Thesis, Harvard University, (1983)

  44. Thomas, W.: Automata on infinite objects, Handbook of Theoretical Computer Science, Volume B: Formal Models and Semantics, pp. 133–192 (1990)

  45. Wolper, P., Vardi, M.Y., Sistla, A.P.: Reasoning about infinite computation paths, Annual Symposium on Foundations of Computer Science (SFCS’83), ACM, pp. 185–194

  46. Wolper, P.: Temporal logic can be more expressive. Inform. Contl. 56(1/2), 72–99 (1983)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

We would like to thank Dogan Ulus for his contributions to the earlier stages of this project. We would also like to thank Kim Guldtrand Larsen, Ioannis Filippidis, Armin Bierre and Jaco van de Pol for sharing their BDD expertise with us.

Author information

Authors and Affiliations

  1. Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA

    Klaus Havelund

  2. Department of Computer Science, Bar Ilan University, Ramat Gan, Israel

    Doron Peled

Authors
  1. Klaus Havelund
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Doron Peled
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Doron Peled.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The research performed by the first author was carried out at Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. The research performed by the second author was partially funded by Israeli Science Foundation Grant 1464/18: “Efficient Runtime Verification for Systems with Lots of Data and its Applications”.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Havelund, K., Peled, D. An extension of first-order LTL with rules with application to runtime verification. Int J Softw Tools Technol Transfer 23, 547–563 (2021). https://doi.org/10.1007/s10009-021-00626-y

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10009-021-00626-y

Keywords

Search

Navigation