Skip to main content
Book cover

International Joint Conference on Automated Reasoning

IJCAR 2016: Automated Reasoning pp 516–531Cite as

Unbounded-Thread Program Verification using Thread-State Equations

Part of the Lecture Notes in Computer Science book series (LNAI,volume 9706)

Abstract

Infinite-state reachability problems arising from unbounded-thread program verification are of great practical importance, yet algorithmically hard. Despite the remarkable success of explicit-state exploration methods to solve such problems, there is a sense that SMT technology can be beneficial to speed up the decision making. This vision was pioneered in recent work by Esparza et al. on SMT-based coverability analysis of Petri nets. We present here an approximate coverability method that operates on thread-transition systems, a model naturally derived from predicate abstractions of multi-threaded programs. In addition to successfully proving uncoverability for all our safe benchmark programs, our approach extends previous work by the ability to decide the unsafety of many unsafe programs, and to provide a witness path. We also demonstrate experimentally that our method beats all leading explicit-state techniques on safe benchmarks and is competitive on unsafe ones, promising to be a very accurate and fast coverability analyzer.

Keywords

  • Unsafe Ones
  • Witness Path
  • Explicit State Exploration
  • Unsafe Instances
  • Initial Shared State

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This work is supported by NSF grant no. CCF-1253331.

This is a preview of subscription content, access via your institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-319-40229-1_35
  • Chapter length: 16 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   69.99
Price excludes VAT (USA)
  • ISBN: 978-3-319-40229-1
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   89.99
Price excludes VAT (USA)
Learn about institutional subscriptions
Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.

Notes

  1. 1.

    Available at www.cprover.org/bfc/; github.com/pierreganty/mist; and http://www.mpi-sws.org/~fniksic/cav2014/repository.tgz.

  2. 2.

    www.cprover.org/bfc/.

  3. 3.

    Petrinizer offers four methods; we use the most powerful: refinement over integers.

References

  1. Abdulla, P.A., Haziza, F., Holík, L.: All for the price of few (parameterized verification through view abstraction). In: Giacobazzi, R., Berdine, J., Mastroeni, I. (eds.) VMCAI 2013. LNCS, vol. 7737, pp. 476–495. Springer, Heidelberg (2013)

    CrossRef  Google Scholar 

  2. Abdulla, P.A.: Well (and better) quasi-ordered transition systems. Bull. Symbolic Logic 16(4), 457–515 (2010)

    MathSciNet  CrossRef  MATH  Google Scholar 

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

    Google Scholar 

  4. Cardoza, E., Lipton, R.J., Meyer, A.R.: Exponential space complete problems for petri nets and commutative semigroups: preliminary report. In: STOC, pp. 50–54 (1976)

    Google Scholar 

  5. Donaldson, A., Kaiser, A., Kroening, D., Wahl, T.: Symmetry-aware predicate abstraction for shared-variable concurrent programs. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 356–371. Springer, Heidelberg (2011)

    CrossRef  Google Scholar 

  6. Esparza, J., Ledesma-Garza, R., Majumdar, R., Meyer, P., Niksic, F.: An SMT-based approach to coverability analysis. In: Biere, A., Bloem, R. (eds.) CAV 2014. LNCS, vol. 8559, pp. 603–619. Springer, Heidelberg (2014)

    Google Scholar 

  7. Esparza, J., Meyer, P.J.: An SMT-based approach to fair termination analysis. In: FMCAD, pp. 49–56 (2015)

    Google Scholar 

  8. Even, S.: Graph Algorithms. W. H. Freeman & Co., New York (1979)

    MATH  Google Scholar 

  9. Finkel, A., Schnoebelen, P.: Well-structured transition systems everywhere!. Theor. Comput. Sci. 256(1–2), 63–92 (2001)

    MathSciNet  CrossRef  MATH  Google Scholar 

  10. Ganty, P., Raskin, J.F., Van Begin, L.: From many places to few: automatic abstraction refinement for petri nets. Fundam. Inf. 88(3), 275–305 (2008)

    MathSciNet  MATH  Google Scholar 

  11. Geeraerts, G., Raskin, J.F., Begin, L.V.: Expand, Enlarge and Check: New algorithms for the coverability problem of WSTS. J. Comput. Syst. Sci. 72(1), 180–203 (2006)

    MathSciNet  CrossRef  MATH  Google Scholar 

  12. Geeraerts, G., Raskin, J.-F., Van Begin, L.: On the efficient computation of the minimal coverability set for petri nets. In: Namjoshi, K.S., Yoneda, T., Higashino, T., Okamura, Y. (eds.) ATVA 2007. LNCS, vol. 4762, pp. 98–113. Springer, Heidelberg (2007)

    CrossRef  Google Scholar 

  13. German, S.M., Sistla, A.P.: Reasoning about systems with many processes. J. ACM 39(3), 675–735 (1992)

    MathSciNet  CrossRef  MATH  Google Scholar 

  14. Hajdu, Á., Vörös, A., Bartha, T.: New search strategies for the petri net CEGAR approach. In: Devillers, R., Valmari, A. (eds.) PETRI NETS 2015. LNCS, vol. 9115, pp. 309–328. Springer, Heidelberg (2015)

    CrossRef  Google Scholar 

  15. Kaiser, A., Kroening, D., Wahl, T.: A widening approach to multithreaded program verification. ACM Trans. Program. Lang. Syst. 36(4), 14 (2014)

    CrossRef  Google Scholar 

  16. Karp, R.M., Miller, R.E.: Parallel program schemata. J. Comput. Syst. Sci. 3(2), 147–195 (1969)

    MathSciNet  CrossRef  MATH  Google Scholar 

  17. Kloos, J., Majumdar, R., Niksic, F., Piskac, R.: Incremental, inductive coverability. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 158–173. Springer, Heidelberg (2013)

    CrossRef  Google Scholar 

  18. Liu, P.: www.ccs.neu.edu/home/lpzun/tse/

  19. Liu, P., Wahl, T.: Infinite-state backward exploration of Boolean broadcast programs. In: FMCAD, pp. 155–162 (2014)

    Google Scholar 

  20. de Moura, L., Bjørner, N.S.: Z3: an efficient SMT solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008)

    CrossRef  Google Scholar 

  21. Rackoff, C.: The covering and boundedness problems for vector addition systems. Theor. Comput. Sci. 6, 223–231 (1978)

    MathSciNet  CrossRef  MATH  Google Scholar 

  22. Reynier, P.-A., Servais, F.: Minimal coverability set for petri nets: Karp and Miller algorithm with pruning. In: Kristensen, L.M., Petrucci, L. (eds.) PETRI NETS 2011. LNCS, vol. 6709, pp. 69–88. Springer, Heidelberg (2011)

    CrossRef  Google Scholar 

  23. Valmari, A., Hansen, H.: Old and new algorithms for minimal coverability sets. In: Haddad, S., Pomello, L. (eds.) PETRI NETS 2012. LNCS, vol. 7347, pp. 208–227. Springer, Heidelberg (2012)

    CrossRef  Google Scholar 

  24. Wimmel, H., Wolf, K.: Applying CEGAR to the petri net state equation. Log. Methods Comput. Sci. 8(3), 827–846 (2012)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Northeastern University, Boston, USA

    Konstantinos Athanasiou, Peizun Liu & Thomas Wahl

Authors
  1. Konstantinos Athanasiou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Peizun Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Thomas Wahl
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Konstantinos Athanasiou .

Editor information

Editors and Affiliations

  1. Aix-Marseille University, Marseille, France

    Nicola Olivetti

  2. SRI International, Menlo Park, California, USA

    Ashish Tiwari

Rights and permissions

Reprints and Permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Athanasiou, K., Liu, P., Wahl, T. (2016). Unbounded-Thread Program Verification using Thread-State Equations. In: Olivetti, N., Tiwari, A. (eds) Automated Reasoning. IJCAR 2016. Lecture Notes in Computer Science(), vol 9706. Springer, Cham. https://doi.org/10.1007/978-3-319-40229-1_35

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-40229-1_35

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40228-4

  • Online ISBN: 978-3-319-40229-1

  • eBook Packages: Computer ScienceComputer Science (R0)