Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Combining the Temporal and Epistemic Dimensions for MTL Monitoring

  • Conference paper
  • First Online:
Formal Modeling and Analysis of Timed Systems (FORMATS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10419))

Abstract

We define a new notion of satisfaction of a temporal logic formula \(\varphi \) by a behavior w. This notion, denoted by \((w,t,t')\,\models \, \varphi \), is characterized by two time parameters: the position t from which satisfaction is considered, and the end of the (finite) behavior \(t'\) which indicates how much do we know about the behavior. We define this notion in dense time where \(\varphi \) is a formula in the future fragment of metric temporal logic (MTL) and w is a Boolean signal of bounded variability. We show that the set of all pairs \((t,t')\) such that \((w,t,t')\,\models \, \varphi \) can be expressed as a finite union of two-dimensional zones and give an effective procedure to compute it.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Similar content being viewed by others

Notes

  1. 1.

    In the context of reactive systems, finite behaviors are sometimes even considered anomalous, representing deadlocks.

  2. 2.

    By a slight abuse of notation we use the same symbol for a formula and its satisfaction signal.

  3. 3.

    It means that if a constraint \(f(t,t')\le c\) is implied by other constraints, the constraint \(f(t,t')\le c-\varepsilon \) is not implied by them for any \(\varepsilon >0\).

References

  1. Abarbanel, Y., Beer, I., Gluhovsky, L., Keidar, S., Wolfsthal, Y.: FoCs – automatic generation of simulation checkers from formal specifications. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 538–542. Springer, Heidelberg (2000). doi:10.1007/10722167_40

    Chapter  Google Scholar 

  2. Basin, D.A., Klaedtke, F., Zalinescu, E.: Failure-aware runtime verification of distributed systems. In: FSTTCS, pp. 590–603 (2015)

    Google Scholar 

  3. Bauer, A., Leucker, M., Schallhart, C.: Monitoring of real-time properties. In: Arun-Kumar, S., Garg, N. (eds.) FSTTCS 2006. LNCS, vol. 4337, pp. 260–272. Springer, Heidelberg (2006). doi:10.1007/11944836_25

    Chapter  Google Scholar 

  4. Blake, A.: Canonical expressions in Boolean algebra. Ph.D. thesis (1938)

    Google Scholar 

  5. Brown, F.M.: Boolean Reasoning: The Logic of Boolean Equations. Springer, New York (2012). doi:10.1007/978-1-4757-2078-5

    MATH  Google Scholar 

  6. De Giacomo, G., Vardi, M.Y.: Linear temporal logic and linear dynamic logic on finite traces. In: IJCAI, pp. 854–860 (2013)

    Google Scholar 

  7. D’Souza, D., Tabareau, N.: On timed automata with input-determined guards. In: Lakhnech, Y., Yovine, S. (eds.) FORMATS/FTRTFT -2004. LNCS, vol. 3253, pp. 68–83. Springer, Heidelberg (2004). doi:10.1007/978-3-540-30206-3_7

    Chapter  Google Scholar 

  8. Eisner, C., Fisman, D., Havlicek, J.: A topological characterization of weakness. In: PODC, pp. 1–8 (2005)

    Google Scholar 

  9. Eisner, C., Fisman, D., Havlicek, J., Lustig, Y., McIsaac, A., Campenhout, D.: Reasoning with temporal logic on truncated paths. In: Hunt, W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 27–39. Springer, Heidelberg (2003). doi:10.1007/978-3-540-45069-6_3

    Chapter  Google Scholar 

  10. Guelev, D.P., Dima, C., Enea, C.: An alternating-time temporal logic with knowledge, perfect recall and past: axiomatisation and model-checking. J. Appl. Non Class. Log. 21(1), 93–131 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  11. Halpern, J.Y., Shoham, Y.: A propositional modal logic of time intervals. J. ACM (JACM) 38(4), 935–962 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  12. Halpern, J.Y., Vardi, M.Y.: The complexity of reasoning about knowledge and time. I. lower bounds. J. Comput. Syst. Sci. 38(1), 195–237 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  13. Kamp, H.: Tense logic and the theory of order. Ph.D. thesis, UCLA (1968)

    Google Scholar 

  14. Konrad, S., Cheng, B.H.C.: Real-time specification patterns. In: ICSE, pp. 372–381 (2005)

    Google Scholar 

  15. Koymans, R.: Specifying real-time properties with metric temporal logic. Real Time Syst. 2(4), 255–299 (1990)

    Article  Google Scholar 

  16. Maler, O.: Some thoughts on runtime verification. In: Falcone, Y., Sánchez, C. (eds.) RV 2016. LNCS, vol. 10012, pp. 3–14. Springer, Cham (2016). doi:10.1007/978-3-319-46982-9_1

    Chapter  Google Scholar 

  17. 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). doi:10.1007/978-3-540-30206-3_12

    Chapter  Google Scholar 

  18. Maler, O., Nickovic, D., Pnueli, A.: Real time temporal logic: past, present, future. In: Pettersson, P., Yi, W. (eds.) FORMATS 2005. LNCS, vol. 3829, pp. 2–16. Springer, Heidelberg (2005). doi:10.1007/11603009_2

    Chapter  Google Scholar 

  19. Maler, O., Nickovic, D., Pnueli, A.: From MITL to timed automata. In: Asarin, E., Bouyer, P. (eds.) FORMATS 2006. LNCS, vol. 4202, pp. 274–289. Springer, Heidelberg (2006). doi:10.1007/11867340_20

    Chapter  Google Scholar 

  20. 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). doi:10.1007/978-3-540-78127-1_26

    Chapter  Google Scholar 

  21. Manna, Z., Pnueli, A.: The anchored version of the temporal framework. In: Bakker, J.W., Roever, W.-P., Rozenberg, G. (eds.) REX 1988. LNCS, vol. 354, pp. 201–284. Springer, Heidelberg (1989). doi:10.1007/BFb0013024

    Chapter  Google Scholar 

  22. Nickovic, D.: Checking timed and hybrid properties: theory and applications. Ph.D. thesis, Université Joseph Fourier, Grenoble, France (2008)

    Google Scholar 

  23. Nivat, M., Perrin, D.: Ensembles reconnaissables de mots bi-infinis. In: STOC, pp. 47–59. ACM (1982)

    Google Scholar 

  24. Pnueli, A.: The temporal logic of programs. In: FOCS, pp. 46–57 (1977)

    Google Scholar 

  25. Pnueli, A.: The temporal semantics of concurrent programs. Theor. Comput. Sci. 13, 45–60 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  26. Prior, A.N.: Past, present and future, vol. 154 (1967)

    Google Scholar 

  27. Reinbacher, T., Rozier, K.Y., Schumann, J.: Temporal-logic based runtime observer pairs for system health management of real-time systems. In: Ábrahám, E., Havelund, K. (eds.) TACAS 2014. LNCS, vol. 8413, pp. 357–372. Springer, Heidelberg (2014). doi:10.1007/978-3-642-54862-8_24

    Chapter  Google Scholar 

  28. 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 

  29. Van Benthem, J., Pacuit, E.: The tree of knowledge in action: towards a common perspective (2006)

    Google Scholar 

  30. 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

    Chapter  Google Scholar 

  31. Vardi, M.Y., Wolper, P.: An automata-theoretic approach to automatic program verification. In: LICS (1986)

    Google Scholar 

  32. Venema, Y.: A modal logic for chopping intervals. J. Log. Comput. 1(4), 453–476 (1991)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. IRIF, Paris Diderot University, Paris, France

    Eugene Asarin

  2. Verimag, CNRS/University of Grenoble-Alpes, Grenoble, France

    Oded Maler & Dogan Ulus

  3. Austrian Institute of Technology, Vienna, Austria

    Dejan Nickovic

Authors
  1. Eugene Asarin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Oded Maler
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Dejan Nickovic
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Dogan Ulus
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dogan Ulus .

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Oxford, Oxford, United Kingdom

    Alessandro Abate

  2. Dept. d’Informatique, Université Libre de Bruxelles, Brussels, Belgium

    Gilles Geeraerts

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Asarin, E., Maler, O., Nickovic, D., Ulus, D. (2017). Combining the Temporal and Epistemic Dimensions for MTL Monitoring. In: Abate, A., Geeraerts, G. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2017. Lecture Notes in Computer Science(), vol 10419. Springer, Cham. https://doi.org/10.1007/978-3-319-65765-3_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-65765-3_12

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-65764-6

  • Online ISBN: 978-3-319-65765-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation