Skip to main content

Loop Summarization Using Abstract Transformers

  • Conference paper
Automated Technology for Verification and Analysis (ATVA 2008)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 5311))

Abstract

Existing program analysis tools that implement abstraction rely on saturating procedures to compute over-approximations of fixpoints. As an alternative, we propose a new algorithm to compute an over-approximation of the set of reachable states of a program by replacing loops in the control flow graph by their abstract transformer. Our technique is able to generate diagnostic information in case of property violations, which we call leaping counterexamples. We have implemented this technique and report experimental results on a set of large ANSI-C programs using abstract domains that focus on properties related to string-buffers.

Supported by the Swiss National Science Foundation grant no. 200021-111687 and an award from IBM research.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

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. Cousot, P., Cousot, R.: Abstract interpretation: A unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: POPL, pp. 238–252 (1977)

    Google Scholar 

  2. Cousot, P., Halbwachs, N.: Automatic Discovery of Linear Restraints Among Variables of a Program. In: POPL, pp. 84–96 (1978)

    Google Scholar 

  3. Cousot, P., Cousot, R.: Comparing the Galois connection and widening/narrowing approaches to abstract interpretation. In: Bruynooghe, M., Wirsing, M. (eds.) PLILP 1992. LNCS, vol. 631, pp. 269–295. Springer, Heidelberg (1992)

    Chapter  Google Scholar 

  4. Reps, T.W., Sagiv, S., Yorsh, G.: Symbolic Implementation of the Best Transformer. In: Steffen, B., Levi, G. (eds.) VMCAI 2004. LNCS, vol. 2937, pp. 252–266. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  5. Clarke, E.M., Kroening, D., Sharygina, N., Yorav, K.: Predicate abstraction of ANSI-C programs using SAT. FMSD 25, 105–127 (2004)

    MATH  Google Scholar 

  6. Gopan, D., Reps, T.W.: Low-level library analysis and summarization. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 68–81. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  7. Sharir, M., Pnueli, A.: Two approaches to interprocedural data flow analysis. In: Program Flow Analysis: theory and applications. Prentice-Hall, Englewood Cliffs (1981)

    Google Scholar 

  8. Aiken, A., Bugrara, S., Dillig, I., Dillig, T., Hackett, B., Hawkins, P.: An overview of the Saturn project. In: PASTE, pp. 43–48. ACM, New York (2007)

    Chapter  Google Scholar 

  9. Babic, D., Hu, A.J.: Calysto: scalable and precise extended static checking. In: ICSE, pp. 211–220. ACM, New York (2008)

    Chapter  Google Scholar 

  10. Jackson, D., Vaziri, M.: Finding bugs with a constraint solver. In: ISSTA, pp. 14–25 (2000)

    Google Scholar 

  11. Clarke, E., Kroening, D., Lerda, F.: A tool for checking ANSI-C programs. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 168–176. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  12. Clarke, E., Grumberg, O., Peled, D.A.: Model checking. MIT Press, Cambridge (1999)

    Google Scholar 

  13. Cousot, P., Cousot, R.: Systematic design of program analysis frameworks. In: POPL, pp. 269–282 (1979)

    Google Scholar 

  14. 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)

    Chapter  Google Scholar 

  15. Lahiri, S.K., Ball, T., Cook, B.: Predicate abstraction via symbolic decision procedures. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 24–38. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  16. Kroening, D., Sharygina, N.: Approximating predicate images for bit-vector logic. In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006. LNCS, vol. 3920, pp. 242–256. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  17. Lahiri, S.K., Nieuwenhuis, R., Oliveras, A.: SMT techniques for fast predicate abstraction. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 424–437. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  18. Cavada, R., Cimatti, A., Franzén, A., Kalyanasundaram, K., Roveri, M., Shyamasundar, R.K.: Computing predicate abstractions by integrating BDDs and SMT solvers. In: FMCAD, pp. 69–76. IEEE, Los Alamitos (2007)

    Google Scholar 

  19. Tarjan, R.E.: Fast algorithms for solving path problems. J. ACM 28, 594–614 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  20. Ashcroft, E., Manna, Z.: The translation of ’go to’ programs to ’while’ programs, pp. 49–61 (1979)

    Google Scholar 

  21. Dor, N., Rodeh, M., Sagiv, S.: CSSV: towards a realistic tool for statically detecting all buffer overflows in C. In: PLDI, pp. 155–167 (2003)

    Google Scholar 

  22. Zitser, M., Lippmann, R., Leek, T.: Testing static analysis tools using exploitable buffer overflows from open source code. In: SIGSOFT FSE, pp. 97–106 (2004)

    Google Scholar 

  23. Ku, K., Hart, T.E., Chechik, M., Lie, D.: A buffer overflow benchmark for software model checkers. In: ASE 2007, pp. 389–392. ACM Press, New York (2007)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kroening, D., Sharygina, N., Tonetta, S., Tsitovich, A., Wintersteiger, C.M. (2008). Loop Summarization Using Abstract Transformers. In: Cha, S.(., Choi, JY., Kim, M., Lee, I., Viswanathan, M. (eds) Automated Technology for Verification and Analysis. ATVA 2008. Lecture Notes in Computer Science, vol 5311. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88387-6_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-88387-6_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-88386-9

  • Online ISBN: 978-3-540-88387-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics