Skip to main content
Springer Nature Link
Log in

Analysing Mu-Calculus Properties of Pushdown Systems

  • Conference paper
Model Checking Software (SPIN 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6349))

Included in the following conference series:

  • 447 Accesses

Abstract

Pushdown systems provide a natural model of software with recursive procedure calls. We provide a tool (PDSolver) implementing an algorithm for computing the winning regions of a pushdown parity game and its adaptation to the direct computation of modal μ-calculus properties over pushdown systems. We also extend the algorithm to allow backwards, as well as forwards, modalities and allow the user to restrict the control flow graph to configurations reachable from a designated initial state. These extensions are motivated by applications in dataflow analysis. We provide two sets of experimental data. First, we obtain a picture of the general behaviour by analysing random problem instances. Secondly, we use the tool to perform dataflow analysis on real-world Java programs, taken from the DaCapo benchmark suite.

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

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. Bouajjani, A., Esparza, J., Maler, O.: Reachability analysis of pushdown automata: Application to model-checking. In: Mazurkiewicz, A., Winkowski, J. (eds.) CONCUR 1997. LNCS, vol. 1243, pp. 135–150. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  2. Lamprecht, A., Margaria, T., Steffen, B.: Data-flow analysis as model checking within the jabc. In: Mycroft, A., Zeller, A. (eds.) CC 2006. LNCS, vol. 3923, pp. 101–104. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  3. Steffen, B.: Data flow analysis as model checking. In: Ito, T., Meyer, A.R. (eds.) TACS 1991. LNCS, vol. 526, pp. 346–365. Springer, Heidelberg (1991)

    Chapter  Google Scholar 

  4. Hague, M., Ong, C.-H.L.: Winning regions of pushdown parity games: A saturation method. In: Bravetti, M., Zavattaro, G. (eds.) CONCUR 2009. LNCS, vol. 5710, pp. 384–398. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  5. Walukiewicz, I.: Pushdown processes: Games and model checking. In: Alur, R., Henzinger, T.A. (eds.) CAV 1996. LNCS, vol. 1102, pp. 62–74. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  6. Bradfield, J.C., Stirling, C.P.: Modal logics and mu-calculi: An introduction. In: Handbook of Process Algebra, pp. 293–330 (2001)

    Google Scholar 

  7. Hague, M., Ong, C.H.L.: A saturation method for the modal mu-calculus with backwards modalities over pushdown systems. arXiv:1006.5906v1 [cs.FL] (2010)

    Google Scholar 

  8. Vallée-Rai, R., Hendren, L., Sundaresan, V., Lam, P., Gagnon, E., Co, P.: Soot - a Java optimization framework. In: CASCON 1999, pp. 125–135 (1999)

    Google Scholar 

  9. Blackburn, S.M., et al.: The DaCapo benchmarks: Java benchmarking development and analysis. In: OOPSLA 2006, pp. 169–190 (2006)

    Google Scholar 

  10. Schwoon, S.: Model-checking Pushdown Systems. PhD thesis, Technical University of Munich (2002)

    Google Scholar 

  11. Ball, T., Rajamani, S.K.: Bebop: A symbolic model checker for boolean programs. In: Havelund, K., Penix, J., Visser, W. (eds.) SPIN 2000. LNCS, vol. 1885, pp. 113–130. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  12. Ball, T., Rajamani, S.K.: The SLAM project: Debugging system software via static analysis. In: POPL 2002, pp. 1–3 (2002)

    Google Scholar 

  13. Cachat, T.: Higher order pushdown automata, the caucal hierarchy of graphs and parity games. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 556–569. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  14. Reps, T., Schwoon, S., Jha, S., Melski, D.: Weighted pushdown systems and their application to interprocedural dataflow analysis. Sci. Comput. Program. 58(1-2), 206–263 (2005)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computing Laboratory, Oxford University, UK

    Matthew Hague & C. -H. Luke Ong

Authors
  1. Matthew Hague
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. -H. Luke Ong
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Formal Methods and Tools, Department of Computer Science, University of Twente, P.O. Box 217, 7500AE, Enschede, The Netherlands

    Jaco van de Pol  & Michael Weber  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hague, M., Ong, C.H.L. (2010). Analysing Mu-Calculus Properties of Pushdown Systems. In: van de Pol, J., Weber, M. (eds) Model Checking Software. SPIN 2010. Lecture Notes in Computer Science, vol 6349. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16164-3_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-16164-3_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16163-6

  • Online ISBN: 978-3-642-16164-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics