Sliced Path Prefixes: An Effective Method to Enable Refinement Selection

  • Dirk Beyer
  • Stefan Löwe
  • Philipp Wendler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9039)


Automatic software verification relies on constructing, for a given program, an abstract model that is (1) abstract enough to avoid state-space explosion and (2) precise enough to reason about the specification. Counterexample-guided abstraction refinement is a standard technique that suggests to extract information from infeasible error paths, in order to refine the abstract model if it is too imprecise. Existing approaches —including our previous work— do not choose the refinement for a given path systematically. We present a method that generates alternative refinements and allows to systematically choose a suited one. The method takes as input one given infeasible error path and applies a slicing technique to obtain a set of new error paths that are more abstract than the original error path but still infeasible, each for a different reason. The (more abstract) constraints of the new paths can be passed to a standard refinement procedure, in order to obtain a set of possible refinements, one for each new path. Our technique is completely independent from the abstract domain that is used in the program analysis, and does not rely on a certain proof technique, such as SMT solving. We implemented the new algorithm in the verification framework CPAchecker and made our extension publicly available. The experimental evaluation of our technique indicates that there is a wide range of possibilities on how to refine the abstract model for a given error path, and we demonstrate that the choice of which refinement to apply to the abstract model has a significant impact on the verification effectiveness and efficiency.


Abstract Model Interpolation Problem Program Location Abstract Domain Constraint Sequence 
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.


  1. 1.
    Albarghouthi, A., Li, Y., Gurfinkel, A., Chechik, M.: Ufo: A framework for abstraction- and interpolation-based software verification. In: Madhusudan, P., Seshia, S.A. (eds.) CAV 2012. LNCS, vol. 7358, pp. 672–678. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  2. 2.
    Alberti, F., Bruttomesso, R., Ghilardi, S., Ranise, S., Sharygina, N.: An extension of lazy abstraction with interpolation for programs with arrays. Formal Methods in System Design 45(1), 63–109 (2014)CrossRefzbMATHGoogle Scholar
  3. 3.
    Apel, S., Beyer, D., Friedberger, K., Raimondi, F., von Rhein, A.: Domain types: Abstract-domain selection based on variable usage. In: Bertacco, V., Legay, A. (eds.) HVC 2013. LNCS, vol. 8244, pp. 262–278. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  4. 4.
    Ball, T., Cook, B., Levin, V., Rajamani, S.K.: SLAM and Static Driver Verifier: Technology transfer of formal methods inside Microsoft. In: Boiten, E.A., Derrick, J., Smith, G.P. (eds.) IFM 2004. LNCS, vol. 2999, pp. 1–20. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  5. 5.
    Ball, T., Rajamani, S.K.: The Slam project: Debugging system software via static analysis. In: Launchbury, J., Mitchell, J.C. (eds.) POPL, pp. 1–3. ACM, New York (2002)Google Scholar
  6. 6.
    Beyer, D.: Software verification and verifiable witnesses (Report on SV-COMP 2015). In: Baier, C., Tinelli, C. (eds.) TACAS 2015. LNCS, vol. 9035, pp. 401–416. Springer, Heidelberg (2015)CrossRefGoogle Scholar
  7. 7.
    Beyer, D., Henzinger, T.A., Jhala, R., Majumdar, R.: The software model checker Blast. Int. J. Softw. Tools Technol. Transfer 9(5-6), 505–525 (2007)CrossRefGoogle Scholar
  8. 8.
    Beyer, D., Henzinger, T.A., Majumdar, R., Rybalchenko, A.: Path invariants. In: Ferrante, J., McKinley, K.S. (eds.) PLDI, pp. 300–309. ACM, New York (2007)Google Scholar
  9. 9.
    Beyer, D., Henzinger, T.A., Théoduloz, G.: Program analysis with dynamic precision adjustment. In: ASE, pp. 29–38. IEEE, Washington, DC (2008)Google Scholar
  10. 10.
    Beyer, D., Keremoglu, M.E.: CPAchecker: A tool for configurable software verification. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 184–190. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  11. 11.
    Beyer, D., Löwe, S.: Explicit-state software model checking based on CEGAR and interpolation. In: Cortellessa, V., Varró, D. (eds.) FASE 2013. LNCS, vol. 7793, pp. 146–162. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  12. 12.
    Beyer, D., Löwe, S., Wendler, P.: Domain-type-guided refinement selection based on sliced path prefixes. Technical Report MIP-1501, University of Passau (January 2015), arXiv:1502.00045Google Scholar
  13. 13.
    Beyer, D., Petrenko, A.K.: Linux driver verification. In: Margaria, T., Steffen, B. (eds.) ISoLA 2012, Part II. LNCS, vol. 7610, pp. 1–6. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  14. 14.
    Blanchet, B., Cousot, P., Cousot, R., Feret, J., Mauborgne, L., Miné, A., Monniaux, D., Rival, X.: A static analyzer for large safety-critical software. In: Cytron, R., Gupta, R. (eds.) PLDI, pp. 196–207. ACM, New York (2003)Google Scholar
  15. 15.
    Clarke, E.M., Grumberg, O., Jha, S., Lu, Y., Veith, H.: Counterexample-guided abstraction refinement for symbolic model checking. J. ACM 50(5), 752–794 (2003)CrossRefMathSciNetGoogle Scholar
  16. 16.
    Craig, W.: Linear reasoning. A new form of the Herbrand-Gentzen theorem. J. Symb. Log. 22(3), 250–268 (1957)CrossRefzbMATHMathSciNetGoogle Scholar
  17. 17.
    D’Silva, V., Kröning, D., Purandare, M., Weissenbacher, G.: Interpolant strength. In: Barthe, G., Hermenegildo, M. (eds.) VMCAI 2010. LNCS, vol. 5944, pp. 129–145. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  18. 18.
    Graf, S., Saïdi, H.: Construction of abstract state graphs with PVS. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 72–83. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  19. 19.
    Henzinger, T.A., Jhala, R., Majumdar, R., McMillan, K.L.: Abstractions from proofs. In: Jones, N.D., Leroy, X. (eds.) POPL, pp. 232–244. ACM, New York (2004)Google Scholar
  20. 20.
    Henzinger, T.A., Jhala, R., Majumdar, R., Sutre, G.: Lazy abstraction. In: Launchbury, J., Mitchell, J.C. (eds.) POPL, pp. 58–70. ACM, New York (2002)Google Scholar
  21. 21.
    Jhala, R., Majumdar, R.: Path slicing. In: Sarkar, V., Hall, M. (eds.) PLDI, pp. 38–47. ACM, New York (2005)Google Scholar
  22. 22.
    Rümmer, P., Subotic, P.: Exploring interpolants. In: Jobstmann, B., Ray, S. (eds.) FMCAD, pp. 69–76. IEEE, Washington, DC (2013)Google Scholar

Copyright information

© IFIP International Federation for Information Processing 2015

Authors and Affiliations

  • Dirk Beyer
    • 1
  • Stefan Löwe
    • 1
  • Philipp Wendler
    • 1
  1. 1.University of PassauPassauGermany

Personalised recommendations