Skip to main content
SpringerLink
Log in

Exemplifying Parametric Timed Specifications over Signals with Bounded Behavior

  • Conference paper
  • First Online:
NASA Formal Methods (NFM 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13260))

Included in the following conference series:

Abstract

Specifying properties can be challenging work. In this paper, we propose an automated approach to exemplify properties given in the form of automata extended with timing constraints and timing parameters, and that can also encode constraints over real-valued signals. That is, given such a specification and given an admissible automaton for each signal, we output concrete runs exemplifying real (or impossible) runs for this specification. Specifically, our method takes as input a specification, and a set of admissible behaviors, all given as a subclass of rectangular hybrid automata, namely timed automata extended with arbitrary clock rates, signal constraints, and timing parameters. Our method then generates concrete runs exemplifying the specification.

This work is partially supported by ERATO HASUO Metamathematics for Systems Design Project (No. JPMJER1603), JST and by the ANR-NRF French-Singaporean research program ProMiS (ANR-19-CE25-0015).

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 109.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 139.99
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.

    Source code, models and results are available at 10.5281/zenodo.6382893.

References

  1. Alur, R., et al.: The algorithmic analysis of hybrid systems. TCS 138(1), 3–34 (1995). https://doi.org/10.1016/0304-3975(94)00202-T

    Article  MathSciNet  MATH  Google Scholar 

  2. Alur, R., Dill, D.L.: A theory of timed automata. TCS 126(2), 183–235 (1994). https://doi.org/10.1016/0304-3975(94)90010-8

    Article  MathSciNet  MATH  Google Scholar 

  3. Alur, R., Henzinger, T.A., Vardi, M.Y.: Parametric real-time reasoning. In: Kosaraju, S.R., Johnson, D.S., Aggarwal, A. (eds.) STOC, pp. 592–601. ACM, New York (1993). https://doi.org/10.1145/167088.167242

  4. André, É.: Parametric deadlock-freeness checking timed automata. In: Sampaio, A., Wang, F. (eds.) ICTAC 2016. LNCS, vol. 9965, pp. 469–478. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-46750-4_27

    Chapter  Google Scholar 

  5. André, É.: IMITATOR 3: synthesis of timing parameters beyond decidability. In: Silva, A., Leino, K.R.M. (eds.) CAV 2021. LNCS, vol. 12759, pp. 552–565. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-81685-8_26

    Chapter  Google Scholar 

  6. André, É., Arias, J., Petrucci, L., Pol, J.: Iterative bounded synthesis for efficient cycle detection in parametric timed automata. In: TACAS 2021. LNCS, vol. 12651, pp. 311–329. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-72016-2_17

    Chapter  MATH  Google Scholar 

  7. André, É., Bloemen, V., Petrucci, L., van de Pol, J.: Minimal-time synthesis for parametric timed automata. In: Vojnar, T., Zhang, L. (eds.) TACAS 2019. LNCS, vol. 11428, pp. 211–228. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17465-1_12

    Chapter  Google Scholar 

  8. André, É., Chatain, T., Encrenaz, E., Fribourg, L.: An inverse method for parametric timed automata. Int. J. Found. Comput. Sci. 20(5), 819–836 (2009). https://doi.org/10.1142/S0129054109006905

    Article  MathSciNet  MATH  Google Scholar 

  9. André, É., Lime, D.: Liveness in L/U-parametric timed automata. In: Legay, A., Schneider, K. (eds.) ACSD, pp. 9–18. IEEE (2017). https://doi.org/10.1109/ACSD.2017.19

  10. André, É., Waga, M., Urabe, N., Hasuo, I.: Exemplifying parametric timed specifications over signals with bounded behavior. Technical report abs/2203.13247, arXiv (2022). https://arxiv.org/abs/2203.13247

  11. Asarin, E., Caspi, P., Maler, O.: Timed regular expressions. J. ACM 49(2), 172–206 (2002). https://doi.org/10.1145/506147.506151

    Article  MathSciNet  MATH  Google Scholar 

  12. Bagnara, R., M., H.P., Zaffanella, E.: The parma polyhedra library: toward a complete set of numerical abstractions for the analysis and verification of hardware and software systems. Sci. Comput. Programm. 72(1–2), 3–21 (2008). https://doi.org/10.1016/j.scico.2007.08.001

  13. Barbot, B., Basset, N., Dang, T., Donzé, A., Kapinski, J., Yamaguchi, T.: Falsification of cyber-physical systems with constrained signal spaces. In: Lee, R., Jha, S., Mavridou, A., Giannakopoulou, D. (eds.) NFM 2020. LNCS, vol. 12229, pp. 420–439. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-55754-6_25

    Chapter  Google Scholar 

  14. Basset, N., Dang, T., Gigler, F., Mateis, C., Ničković, D.: Sampling of shape expressions with ShapEx. In: Arun-Kumar, S., Méry, D., Saha, I., Zhang, L. (eds.) MEMOCODE, pp. 118–125. ACM (2021). https://doi.org/10.1145/3487212.3487350

  15. Brihaye, T., Geeraerts, G., Ho, H.-M., Monmege, B.: MightyL: a compositional translation from MITL to timed automata. In: Majumdar, R., Kunčak, V. (eds.) CAV 2017. LNCS, vol. 10426, pp. 421–440. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63387-9_21

    Chapter  Google Scholar 

  16. Cassez, F., Larsen, K.: The impressive power of stopwatches. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, pp. 138–152. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-44618-4_12

    Chapter  Google Scholar 

  17. Cimatti, A., Griggio, A., Magnago, E., Roveri, M., Tonetta, S.: Extending nuXmv with timed transition systems and timed temporal properties. In: Dillig, I., Tasiran, S. (eds.) CAV 2019. LNCS, vol. 11561, pp. 376–386. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-25540-4_21

    Chapter  Google Scholar 

  18. Dawes, J.H., Reger, G.: Explaining violations of properties in control-flow temporal logic. In: Finkbeiner, B., Mariani, L. (eds.) RV 2019. LNCS, vol. 11757, pp. 202–220. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-32079-9_12

    Chapter  Google Scholar 

  19. Daws, C., Yovine, S.: Two examples of verification of multirate timed automata with Kronos. In: RTSS, pp. 66–75. IEEE Computer Society (1995). https://doi.org/10.1109/REAL.1995.495197

  20. Halbwachs, N., Proy, Y.-E., Raymond, P.: Verification of linear hybrid systems by means of convex approximations. In: Le Charlier, B. (ed.) SAS 1994. LNCS, vol. 864, pp. 223–237. Springer, Heidelberg (1994). https://doi.org/10.1007/3-540-58485-4_43

    Chapter  Google Scholar 

  21. He, J., Bartocci, E., Ničković, D., Isakovic, H., Grosu, R.: From English to Signal Temporal Logic. Technical report abs/2109.10294, arXiv (2021), https://arxiv.org/abs/2109.10294

  22. Henzinger, T.A.: The theory of hybrid automata. In: LICS, pp. 278–292. IEEE Computer Society (1996). https://doi.org/10.1109/LICS.1996.561342

  23. Hoxha, B., Mavridis, N., Fainekos, G.: VISPEC: a graphical tool for elicitation of MTL requirements. In: IROS, pp. 3486–3492. IEEE (2015). https://doi.org/10.1109/IROS.2015.7353863

  24. Hune, T., Romijn, J., Stoelinga, M., Vaandrager, F.W.: Linear parametric model checking of timed automata. JLAP 52–53, 183–220 (2002). https://doi.org/10.1016/S1567-8326(02)00037-1

    Article  MathSciNet  MATH  Google Scholar 

  25. Jovanović, A., Lime, D., Roux, O.H.: Integer parameter synthesis for real-time systems. TSE 41(5), 445–461 (2015). https://doi.org/10.1109/TSE.2014.2357445

    Article  Google Scholar 

  26. Kim, S.K., Carrington, D.A.: Visualization of formal specifications. In: APSEC, pp. 102–109. IEEE Computer Society (1999). https://doi.org/10.1109/APSEC.1999.809590

  27. Kurshan, R.P.: Transfer of model checking to industrial practice. In: Handbook of Model Checking, pp. 763–793. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-10575-8_23

    Chapter  MATH  Google Scholar 

  28. 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 

  29. 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). https://doi.org/10.1007/11867340_20

    Chapter  MATH  Google Scholar 

  30. Nguyen, H.G., Petrucci, L., van de Pol, J.: Layered and collecting NDFS with subsumption for parametric timed automata. In: Lin, A.W., Sun, J. (eds.) ICECCS, pp. 1–9. IEEE Computer Society, December 2018. https://doi.org/10.1109/ICECCS2018.2018.00009

  31. Ničković, D., Qin, X., Ferrère, T., Mateis, C., Deshmukh, J.: Shape expressions for specifying and extracting signal features. In: Finkbeiner, B., Mariani, L. (eds.) RV 2019. LNCS, vol. 11757, pp. 292–309. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-32079-9_17

    Chapter  Google Scholar 

  32. Pakonen, A., Buzhinsky, I., Vyatkin, V.: Counterexample visualization and explanation for function block diagrams. In: INDIN, pp. 747–753. IEEE (2018). https://doi.org/10.1109/INDIN.2018.8472025

  33. Prabhakar, P., Lal, R., Kapinski, J.: Automatic trace generation for signal temporal logic. In: RTSS, pp. 208–217. IEEE Computer Society (2018). https://doi.org/10.1109/RTSS.2018.00038

  34. Raskin, J.F.: An introduction to hybrid automata. In: Hristu-Varsakelis, D., Levine, W.S. (eds.) Handbook of Networked and Embedded Control Systems, pp. 491–518. Birkhäuser (2005)

    Google Scholar 

  35. Roehm, H., Heinz, T., Mayer, E.C.: STLInspector: STL validation with guarantees. In: Majumdar, R., Kunčak, V. (eds.) CAV 2017. LNCS, vol. 10426, pp. 225–232. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63387-9_11

    Chapter  Google Scholar 

  36. Tikhonova, U., Manders, M., Boudewijns, R.: Visualization of formal specifications for understanding and debugging an industrial DSL. In: Milazzo, P., Varró, D., Wimmer, M. (eds.) STAF 2016. LNCS, vol. 9946, pp. 179–195. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-50230-4_13

    Chapter  Google Scholar 

  37. Waga, M., André, É., Hasuo, I.: Model-bounded monitoring of hybrid systems. In: Maggio, M., Weimer, J., Farque, M.A., Oishi, M. (eds.) ICCPS, pp. 21–32. ACM (2021). https://doi.org/10.1145/3450267.3450531

Download references

Author information

Authors and Affiliations

  1. Université de Lorraine, CNRS, Inria, LORIA, 54000, Nancy, France

    Étienne André

  2. Kyoto University, Kyoto, Japan

    Masaki Waga

  3. National Institute of Informatics, Tokyo, Japan

    Natuski Urabe & Ichiro Hasuo

  4. The Graduate University for Advanced Studies, SOKENDAI, Tokyo, Japan

    Ichiro Hasuo

Authors
  1. Étienne André
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Masaki Waga
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Natuski Urabe
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ichiro Hasuo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Étienne André .

Editor information

Editors and Affiliations

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

    Jyotirmoy V. Deshmukh

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

    Klaus Havelund

  3. National Institute of Aerospace, Hampton, VA, USA

    Ivan Perez

Rights and permissions

Reprints and permissions

Copyright information

© 2022 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

André, É., Waga, M., Urabe, N., Hasuo, I. (2022). Exemplifying Parametric Timed Specifications over Signals with Bounded Behavior. In: Deshmukh, J.V., Havelund, K., Perez, I. (eds) NASA Formal Methods. NFM 2022. Lecture Notes in Computer Science, vol 13260. Springer, Cham. https://doi.org/10.1007/978-3-031-06773-0_25

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-06773-0_25

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-06772-3

  • Online ISBN: 978-3-031-06773-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation