[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
Skip to main content

Fixed-Point Methods in Parametric Model Checking

  • Conference paper
Intelligent Systems'2014

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 322))

Abstract

We present a general framework for the synthesis of the constraints under which the selected properties hold in a class of models with discrete transitions, together with Boolean encoding - based method of implementing the theory. We introduce notions of parametric image and preimage, and show how to use them to build fixed-point algorithms for parametric model checking of reachability and deadlock freedom. An outline of how the ideas shown in this paper were specialized for an extension of Computation Tree Logic is given together with some experimental results.

Work partially funded by DEC − 2012/07/N/ST6/03426 NCN Preludium grant.

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

Access this chapter

Subscribe and save

Springer+ Basic
£29.99 /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
GBP 19.95
Price includes VAT (United Kingdom)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
GBP 143.50
Price includes VAT (United Kingdom)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
GBP 179.99
Price includes VAT (United Kingdom)
  • 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Alur, R., Etessami, K., Torre, S.L., Peled, D.: Parametric Temporal Logic for “Model Measuring”. ACM Trans. Comput. Log. 2(3), 388–407 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  2. Alur, R., Henzinger, T., Vardi, M.: Parametric real-time reasoning. In: Proc. of the 25th Ann. Symp. on Theory of Computing (STOC 1993), pp. 592–601. ACM (1993)

    Google Scholar 

  3. Belardinelli, F., Jones, A.V., Lomuscio, A.: Model checking temporal-epistemic logic using alternating tree automata. Fundam. Inform. 112(1), 19–37 (2011)

    MATH  MathSciNet  Google Scholar 

  4. Bozzelli, L., La Torre, S.: Decision problems for lower/upper bound parametric timed automata. Form. Methods Syst. Des. 35(2), 121–151 (2009)

    Article  MATH  Google Scholar 

  5. Bruyère, V., Dall’Olio, E., Raskin, J.F.: Durations, parametric model-checking in timed automata with presburger arithmetic. In: Alt, H., Habib, M. (eds.) STACS 2003. LNCS, vol. 2607, pp. 687–698. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  6. Burch, J.R., Clarke, E., McMillan, K.L., Dill, D.L., Hwang, L.J.: Symbolic model checking: 1020 states and beyond. Information and Computation 98(2), 142–170 (1990)

    Article  MathSciNet  Google Scholar 

  7. Clarke, E.M.: The birth of model checking. In: Grumberg, O., Veith, H. (eds.) 25 Years of Model Checking. LNCS, vol. 5000, pp. 1–26. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  8. Classen, A., Heymans, P., Schobbens, P.Y., Legay, A.: Symbolic model checking of software product lines. In: Proc. of the 33rd Int. Conf. on Software Engineering, ICSE 2011, pp. 321–330. ACM, New York (2011)

    Google Scholar 

  9. Emerson, E.A., Trefler, R.: Parametric quantitative temporal reasoning. In: Proc. of the 14th Symp. on Logic in Computer Science (LICS 1999), pp. 336–343. IEEE Computer Society (July 1999)

    Google Scholar 

  10. Ghallab, M., Nau, D.S., Traverso, P.: Automated planning - theory and practice. Elsevier (2004)

    Google Scholar 

  11. Di Giampaolo, B., La Torre, S., Napoli, M.: Parametric metric interval temporal logic. In: Dediu, A.-H., Fernau, H., Martín-Vide, C. (eds.) LATA 2010. LNCS, vol. 6031, pp. 249–260. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  12. Holzmann, G.J.: Protocol design: Redefining the state of the art. IEEE Software 9(1), 17–22 (1992)

    Article  MathSciNet  Google Scholar 

  13. Jensen, K., Donatelli, S., Koutny, M. (eds.): Transactions on Petri Nets and Other Models of Concurrency IV. LNCS, vol. 6550. Springer, Heidelberg (2010)

    MATH  Google Scholar 

  14. Jones, A.V., Knapik, M., Penczek, W., Lomuscio, A.: Parametric computation tree logic with knowledge. In: Proc. of the Int. Workshop on Concurrency, Specification and Programming (CS&P 2011), pp. 286–300. Białystok University of Technology (2011)

    Google Scholar 

  15. Knapik, M., https://michalknapik.github.io/spatula

  16. Knapik, M., Penczek, W., Szreter, M., Pólrola, A.: Bounded parametric verification for distributed time Petri nets with discrete-time semantics. Fundam. Inform. 101(1-2), 9–27 (2010)

    MATH  Google Scholar 

  17. Knapik, M., Męski, A., Penczek, W.: Action synthesis for branching time logic: Theory and applications. In: Proc. of the 14th Int. Conf. on Application of Concurrency to System Design. IEEE Computer Society (to appear, 2014)

    Google Scholar 

  18. Knapik, M., Szreter, M., Penczek, W.: Bounded parametric model checking for elementary net systems. In: T. Petri Nets and Other Models of Concurrency [13], pp. 42–71

    Google Scholar 

  19. Lin, F.J., Chu, P.M., Liu, M.T.: Protocol verification using reachability analysis: The state space explosion problem and relief strategies. SIGCOMM Comput. Commun. Rev. 17(5), 126–135 (1987)

    Article  Google Scholar 

  20. Pecheur, C., Raimondi, F.: Symbolic model checking of logics with actions. In: Edelkamp, S., Lomuscio, A. (eds.) MoChArt IV. LNCS (LNAI), vol. 4428, pp. 113–128. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  21. Peled, D.: All From One, One For All: On Model Checking Using Representatives. In: Courcoubetis, C. (ed.) CAV 1993. LNCS, vol. 697, pp. 409–423. Springer, Heidelberg (1993)

    Chapter  Google Scholar 

  22. Penczek, W., Pólrola, A., Zbrzezny, A.: Sat-based (parametric) reachability for a class of distributed time petri nets. In: T. Petri Nets and Other Models of Concurrency [13], pp. 72–97

    Google Scholar 

  23. Somenzi, F.: CUDD: CU decision diagram package - release 2.3.1., http://vlsi.colorado.edu/~fabio/CUDD/cuddIntro.html

  24. Wang, F.: Parametric timing analysis for real-time systems. Inf. Comput. 130(2), 131–150 (1996)

    Article  MATH  Google Scholar 

  25. Wang, F.: Parametric analysis of computer systems. Formal Methods in System Design 17(1), 39–60 (2000)

    Article  Google Scholar 

  26. Xie, Y., Aiken, A.: Scalable error detection using boolean satisfiability. SIGPLAN Not. 40(1), 351–363 (2005)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Michał Knapik .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Knapik, M., Penczek, W. (2015). Fixed-Point Methods in Parametric Model Checking. In: Angelov, P., et al. Intelligent Systems'2014. Advances in Intelligent Systems and Computing, vol 322. Springer, Cham. https://doi.org/10.1007/978-3-319-11313-5_22

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-11313-5_22

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-11312-8

  • Online ISBN: 978-3-319-11313-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics