Skip to main content
SpringerLink
Log in

Quantitative Verification of Weighted Kripke Structures

  • Conference paper
Automated Technology for Verification and Analysis (ATVA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 8837))

Abstract

Extending formal verification techniques to handle quantitative aspects, both for the models and for the properties to be checked, has become a central research topic over the last twenty years. Following several recent works, we study model checking for (one-dimensional) weighted Kripke structures with positive and negative weights, and temporal logics constraining the total and/or average weight. We prove decidability when only accumulated weight is constrained, while allowing average-weight constraints alone already is undecidable.

Partly supported by ERC Starting Grant EQualIS and EU FP7 project Cassting.

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 39.99
Price excludes VAT (USA)
  • Available as 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alur, R., Henzinger, T.A.: A really temporal logic. Journal of the ACM 41(1), 181–203 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bohy, A., Bruyère, V., Filiot, E., Raskin, J.-F.: Synthesis from ltl specifications with mean-payoff objectives. In: Piterman, N., Smolka, S.A. (eds.) TACAS 2013 (ETAPS 2013). LNCS, vol. 7795, pp. 169–184. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  3. Boker, U., Chatterjee, K., Henzinger, T.A., Kupferman, O.: Temporal specifications with accumulative values. In: LICS 2011, pp. 43–52. IEEE Comp. Soc. Press (2011)

    Google Scholar 

  4. Bouyer, P., Fahrenberg, U., Larsen, K.G., Markey, N., Srba, J.: Infinite runs in weighted timed automata with energy constraints. In: Cassez, F., Jard, C. (eds.) FORMATS 2008. LNCS, vol. 5215, pp. 33–47. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  5. Bouyer, P., Larsen, K.G., Markey, N.: Lower-bound constrained runs in weighted timed automata. Performance Evaluation 73, 91–109 (2014)

    Article  Google Scholar 

  6. Beyer, D., Lewerentz, C., Noack, A.: Rabbit: A tool for BDD-based verification of real-time systems. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 122–125. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  7. Bouyer, P., Markey, N., Olschewski, J., Ummels, M.: Measuring permissiveness in parity games: Mean-payoff parity games revisited. In: Bultan, T., Hsiung, P.-A. (eds.) ATVA 2011. LNCS, vol. 6996, pp. 135–149. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  8. Campos, S.V.A., Clarke, E.M.: Real-time symbolic model checking for discrete time models. In: Real-Time Symbolic Model Checking for Discrete Time Models. AMAST Series in Computing, vol. 2, pp. 129–145. World Scientific (1995)

    Google Scholar 

  9. Comon, H., Cortier, V.: Flatness is not a weakness. In: Clote, P.G., Schwichtenberg, H. (eds.) CSL 2000. LNCS, vol. 1862, pp. 262–276. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  10. Chatterjee, K., Doyen, L.: Energy parity games. Theoretical Computer Science 458, 49–60 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  11. Chatterjee, K., Doyen, L., Henzinger, T.A., Raskin, J.-F.: Generalized mean-payoff and energy games. In: FSTTCS 2010. Leibniz International Proceedings in Informatics, vol. 8, Leibniz-Zentrum für Informatik (2010)

    Google Scholar 

  12. Clarke, E.M., Emerson, E.A.: Design and synthesis of synchronization skeletons using branching-time temporal logic. In: Kozen, D. (ed.) Logic of Programs 1981. LNCS, vol. 131, pp. 52–71. Springer, Heidelberg (1982)

    Chapter  Google Scholar 

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

    Google Scholar 

  14. Chatterjee, K., Randour, M., Raskin, J.-F.: Strategy synthesis for multi-dimensional quantitative objectives. In: Koutny, M., Ulidowski, I. (eds.) CONCUR 2012. LNCS, vol. 7454, pp. 115–131. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  15. Demri, S., Gascon, R.: The effects of bounding syntactic resources on Presburger LTL. Journal of Logic and Computation 19(6), 1541–1575 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  16. Demri, S., Lazić, R., Sangnier, A.: Model checking memoryful linear-time logics over one-counter automata. Theoretical Computer Science 411(22-24), 2298–2316 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  17. Emerson, E.A., Mok, A.K.-L., Sistla, A.P., Srinivasan, J.: Quantitative temporal reasoning. Real-Time Systems 4, 331–352 (1992)

    Article  Google Scholar 

  18. Esparza, J., Nielsen, M.: Decidability issues for petri nets - a survey. Bulletin of the EATCS 52, 244–262 (1994)

    Google Scholar 

  19. Göller, S., Haase, C., Ouaknine, J., Worrell, J.: Model checking succinct and parametric one-counter automata. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds.) ICALP 2010. LNCS, vol. 6199, pp. 575–586. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  20. Göller, S., Lohrey, M.: Branching-time model checking of one-counter processes. In: STACS 2010. Leibniz International Proceedings in Informatics, vol. 20, pp. 405–416. Leibniz-Zentrum für Informatik (2010)

    Google Scholar 

  21. Haase, C.: On the Complexity of Model Checking Counter Automata. PhD thesis, University of Oxford, UK (2012)

    Google Scholar 

  22. Haase, C., Kreutzer, S., Ouaknine, J., Worrell, J.: Reachability in succinct and parametric one-counter automata. In: Bravetti, M., Zavattaro, G. (eds.) CONCUR 2009. LNCS, vol. 5710, pp. 369–383. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  23. Jensen, J.F., Larsen, K.G., Srba, J., Oestergaard, L.K.: Local model checking of weighted CTL with upper-bound constraints. In: Bartocci, E., Ramakrishnan, C.R. (eds.) SPIN 2013. LNCS, vol. 7976, pp. 178–195. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

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

    Article  Google Scholar 

  25. Minsky, M.L.: Recursive unsolvability of Post’s problem of ”tag” and other topics in theory of Turing machines. Annals of Mathematics 74(3), 437–455 (1961)

    Article  MathSciNet  MATH  Google Scholar 

  26. Pnueli, A.: The temporal logic of programs. In: FOCS 1977, pp. 46–57. IEEE Comp. Soc. Press (1977)

    Google Scholar 

  27. Queille, J.-P., Sifakis, J.: Specification and verification of concurrent systems in CESAR. In: Dezani-Ciancaglini, M., Montanari, U. (eds.) Programming 1982. LNCS, vol. 137, pp. 337–351. Springer, Heidelberg (1982)

    Chapter  Google Scholar 

  28. Serre, O.: Parity games played on transition graphs of one-counter processes. In: Aceto, L., Ingólfsdóttir, A. (eds.) FOSSACS 2006. LNCS, vol. 3921, pp. 337–351. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  29. Zwick, U., Paterson, M.: The complexity of mean payoff games on graphs. Theoretical Computer Science 158(1-2), 343–359 (1996)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LSV, CNRS & ENS Cachan, France

    Patricia Bouyer, Patrick Gardy & Nicolas Markey

Authors
  1. Patricia Bouyer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Patrick Gardy
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nicolas Markey
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. NICTA, Kensington, NSW, Australia

    Franck Cassez

  2. Départament d’Informatique, Université Libre de Bruxelles (U.L.B.), Belgium

    Jean-François Raskin

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Bouyer, P., Gardy, P., Markey, N. (2014). Quantitative Verification of Weighted Kripke Structures. In: Cassez, F., Raskin, JF. (eds) Automated Technology for Verification and Analysis. ATVA 2014. Lecture Notes in Computer Science, vol 8837. Springer, Cham. https://doi.org/10.1007/978-3-319-11936-6_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-11936-6_6

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-11935-9

  • Online ISBN: 978-3-319-11936-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation