Skip to main content
SpringerLink
Log in

On the Reachability Analysis of Acyclic Networks of Pushdown Systems

  • Conference paper
CONCUR 2008 - Concurrency Theory (CONCUR 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5201))

Included in the following conference series:

Abstract

We address the reachability problem in acyclic networks of pushdown systems. We consider communication based either on shared memory or on message passing through unbounded lossy channels. We prove mainly that the reachability problem between recognizable sets of configurations (i.e., definable by a finite union of products of finite-state automata) is decidable for such networks, and that for lossy channel pushdown networks, the channel language is effectively recognizable. This fact holds although the set of reachable configurations (including stack contents) for a network of depth (at least) 2 is not rational in general (i.e., not definable by a multi-tape finite automaton). Moreover, we prove that for a network of depth 1, the reachability set is rational and effectively constructible (under an additional condition on the topology for lossy channel networks).

Supported by the French projects ANR-06-SETI-001 AVERISS and RNTL AVERILES.

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. Abdulla, P.A., Cerans, K., Jonsson, B., Tsay, Y.-K.: General decidability theorems for infinite-state systems. In: LICS 1996, pp. 313–321 (1996)

    Google Scholar 

  2. Abdulla, P.A., Collomb-Annichini, A., Bouajjani, A., Jonsson, B.: Using forward reachability analysis for verification of lossy channel systems. FMSD 25(1), 39–65 (2004)

    MATH  Google Scholar 

  3. Abdulla, P.A., Jonsson, B.: Verifying programs with unreliable channels. Inf. Comput. 127(2), 91–101 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  4. Atig, M.F., Bouajjani, A., Touili, T.: On the reachability analysis of acyclic networks of pushdown systems. Research report, LIAFA lab (April 2008)

    Google Scholar 

  5. Berstel, J.: Transductions and context-free langages. TeubnerStudienbucher Informatik (1979)

    Google Scholar 

  6. Bouajjani, A., Esparza, J., Schwoon, S., Strejcek, J.: Reachability analysis of multithreaded software with asynchronous communication. In: Ramanujam, R., Sen, S. (eds.) FSTTCS 2005. LNCS, vol. 3821, Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  7. Bouajjani, A., Esparza, J., Touili, T.: A generic approach to the static analysis of concurrent programs with procedures. Int. J. Found. Comput. Sci. 14(4), 551 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  8. Bouajjani, A., Müller-Olm, M., Touili, T.: Regular symbolic analysis of dynamic networks of pushdown systems. In: Abadi, M., de Alfaro, L. (eds.) CONCUR 2005. LNCS, vol. 3653. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  9. Bouajjani, A., Touili, T.: Reachability analysis of process rewrite systems. In: Pandya, P.K., Radhakrishnan, J. (eds.) FSTTCS 2003. LNCS, vol. 2914, pp. 74–87. Springer, Heidelberg (2003)

    Google Scholar 

  10. Bouajjani, A., Touili, T.: On computing reachability sets of process rewrite systems. In: Giesl, J. (ed.) RTA 2005. LNCS, vol. 3467, Springer, Heidelberg (2005)

    Google Scholar 

  11. Bouajjani, A., Esparza, J.: Rewriting models of boolean programs. In: Pfenning, F. (ed.) RTA 2006. LNCS, vol. 4098, pp. 136–150. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  12. Chadha, R., Viswanathan, M.: Decidability results for well-structured transition systems with auxiliary storage. In: Caires, L., Vasconcelos, V.T. (eds.) CONCUR 2007. LNCS, vol. 4703, pp. 136–150. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  13. Chaki, S., Clarke, E.M., Kidd, N., Reps, T.W., Touili, T.: Verifying concurrent message-passing c programs with recursive calls. In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006. LNCS, vol. 3920, pp. 334–349. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  14. Chambard, P., Schnoebelen, P.: Post embedding problem is not primitive recursive, with applications to channel systems. In: Arvind, V., Prasad, S. (eds.) FSTTCS 2007. LNCS, vol. 4855, pp. 265–276. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  15. Esparza, J., Knoop, J.: An automata-theoretic approach to interprocedural dataflow analysis. In: Thomas, W. (ed.) FOSSACS 1999. LNCS, vol. 1578. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  16. Esparza, J., Podelski, A.: Efficient algorithms for pre\(^{\mbox{*}}\) and post\(^{\mbox{*}}\) on interprocedural parallel flow graphs. In: POPL, pp. 1–11 (2000)

    Google Scholar 

  17. Finkel, A., Schnoebelen, P.: Well-structured transition systems everywhere! TCS 256(1-2), 63–92 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  18. Jhala, R., Majumdar, R.: Interprocedural analysis of asynchronous programs. In: POPL. IEEE, Los Alamitos (2007)

    Google Scholar 

  19. Kahlon, V., Ivancic, F., Gupta, A.: Reasoning about threads communicating via locks. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576. Springer, Heidelberg (2005)

    Google Scholar 

  20. La Torre, S., Madhusudan, P., Parlato, G.: Context-bounded analysis of concurrent queue systems. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  21. Lammich, P., Müller-Olm, M.: Precise fixpoint-based analysis of programs with thread-creation and procedures. In: Caires, L., Vasconcelos, V.T. (eds.) CONCUR 2007. LNCS, vol. 4703. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  22. Lugiez, D., Schnoebelen, P.: The regular viewpoint on PA-processes. In: Sangiorgi, D., de Simone, R. (eds.) CONCUR 1998. LNCS, vol. 1466, pp. 50–66. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  23. Mayr, R.: Undecidable problems in unreliable computations. Theor. Comput. Sci. 1-3(297) (2003)

    Google Scholar 

  24. Qadeer, S., Rehof, J.: Context-bounded model checking of concurrent software. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440. Springer, Heidelberg (2005)

    Google Scholar 

  25. Schnoebelen, P.: Verifying lossy channel systems has nonprimitive recursive complexity. Inf. Process. Lett. 83(5) (2002)

    Google Scholar 

  26. Schwoon, S.: Model-Checking Pushdown Systems. PhD thesis, Technische Universität München (2002)

    Google Scholar 

  27. Sen, K., Viswanathan, M.: Model checking multithreaded programs with asynchronous atomic methods. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 300–314. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  28. La Torre, S., Madhusudan, P., Parlato, G.: A robust class of context-sensitive languages. In: LICS, pp. 161–170. IEEE, Los Alamitos (2007)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LIAFA, CNRS & Univ. of Paris 7, Case 7014, 75205, Paris 13, France

    Mohamed Faouzi Atig, Ahmed Bouajjani & Tayssir Touili

Authors
  1. Mohamed Faouzi Atig
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ahmed Bouajjani
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tayssir Touili
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Franck van Breugel Marsha Chechik

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Atig, M.F., Bouajjani, A., Touili, T. (2008). On the Reachability Analysis of Acyclic Networks of Pushdown Systems. In: van Breugel, F., Chechik, M. (eds) CONCUR 2008 - Concurrency Theory. CONCUR 2008. Lecture Notes in Computer Science, vol 5201. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85361-9_29

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-85361-9_29

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-85360-2

  • Online ISBN: 978-3-540-85361-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation