Skip to main content
SpringerLink
Log in
Book cover

Automated Technology for Verification and Analysis pp 240–254Cite as

Integrating Policy Iterations in Abstract Interpreters

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 8172))

Abstract

Among precise abstract interpretation methods developed during the last decade, policy iterations is one of the most promising. Despite its efficiency, it has not yet seen a broad usage in static analyzers. We believe the main explanation to this restrictive use, beside the novelty of the technique, lies in its lack of integration in the classic abstract domain framework. This prevents an easy integration in existing static analyzers and collaboration with other, already implemented, abstract domains through reduced product. This paper aims at providing a classic abstract domain interface to policy iterations.

Usage of semidefinite programming to infer quadratic invariants on linear systems is one of the most appealing use of policy iteration. Combination with a template generation heuristic, inspired from existing methods from control theory, gives a fully automatic abstract domain to infer quadratic invariants on linear systems with guards. Those systems often constitute the core of embedded control systems and are hard, when not impossible, to analyze with linear abstract domains. The method has been implemented and applied to some benchmark systems, giving good results.

This work has been partially supported by the FNRAE Project CAVALE and the ANR INS Project CAFEIN.

This is a preview of subscription content, 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Adjé, A., Gaubert, S., Goubault, E.: Coupling policy iteration with semi-definite relaxation to compute accurate numerical invariants in static analysis. In: Gordon, A.D. (ed.) ESOP 2010. LNCS, vol. 6012, pp. 23–42. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  2. Borchers, B.: Csdp, a c library for semidefinite programming. Optimization Methods and Software 11(1-4) (1999)

    Article  MathSciNet  Google Scholar 

  3. Bouissou, O., Seladji, Y., Chapoutot, A.: Acceleration of the abstract fixpoint computation in numerical program analysis. J. Symb. Comput. 47(12) (2012)

    Article  MathSciNet  Google Scholar 

  4. Bourdoncle, F.: Efficient chaotic iteration strategies with widenings. In: Pottosin, I.V., Bjorner, D., Broy, M. (eds.) FMP&TA 1993. LNCS, vol. 735, pp. 128–141. Springer, Heidelberg (1993)

    Chapter  Google Scholar 

  5. Boyd, S., El Ghaoui, L., Féron, É., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory, vol. 15. SIAM, Philadelphia (1994)

    Book  Google Scholar 

  6. Costan, A., Gaubert, S., Goubault, E., Martel, M., Putot, S.: A policy iteration algorithm for computing fixed points in static analysis of programs. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 462–475. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  7. Cousot, P.: Proving program invariance and termination by parametric abstraction, lagrangian relaxation and semidefinite programming. In: Cousot, R. (ed.) VMCAI 2005. LNCS, vol. 3385, pp. 1–24. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

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

    Google Scholar 

  9. Cousot, P., Cousot, R., Feret, J., Mauborgne, L., Miné, A., Rival, X.: Why does astrée scale up? Formal Methods in System Design 35(3), 229–264 (2009)

    Article  Google Scholar 

  10. Cousot, P., Cousot, R., Feret, J., Mauborgne, L., Miné, A., Monniaux, D., Rival, X.: Combination of abstractions in the Astrée static analyzer. In: Okada, M., Satoh, I. (eds.) ASIAN 2006. LNCS, vol. 4435, pp. 272–300. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  11. Feautrier, P., Gonnord, L.: Accelerated invariant generation for c programs with aspic and c2fsm. Electr. Notes Theor. Comput. Sci. 267(2) (2010)

    Article  Google Scholar 

  12. Feret, J.: Static analysis of digital filters. In: Schmidt, D. (ed.) ESOP 2004. LNCS, vol. 2986, pp. 33–48. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  13. Feret, J.: Numerical abstract domains for digital filters. In: International Workshop on Numerical and Symbolic Abstract Domains, NSAD (2005)

    Google Scholar 

  14. Gaubert, S., Goubault, E., Taly, A., Zennou, S.: Static analysis by policy iteration on relational domains. In: De Nicola, R. (ed.) ESOP 2007. LNCS, vol. 4421, pp. 237–252. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  15. Gawlitza, T., Seidl, H.: Precise fixpoint computation through strategy iteration. In: De Nicola, R. (ed.) ESOP 2007. LNCS, vol. 4421, pp. 300–315. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  16. Gawlitza, T., Seidl, H.: Precise relational invariants through strategy iteration. In: Duparc, J., Henzinger, T.A. (eds.) CSL 2007. LNCS, vol. 4646, pp. 23–40. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  17. Gawlitza, T.M., Monniaux, D.: Improving strategies via SMT solving. In: Barthe, G. (ed.) ESOP 2011. LNCS, vol. 6602, pp. 236–255. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  18. Gawlitza, T.M., Seidl, H.: Computing relaxed abstract semantics w.r.t. Quadratic zones precisely. In: Cousot, R., Martel, M. (eds.) SAS 2010. LNCS, vol. 6337, pp. 271–286. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  19. Gawlitza, T.M., Seidl, H., Adjé, A., Gaubert, S., Goubault, E.: Abstract interpretation meets convex optimization. J. Symb. Comput. 47(12) (2012)

    Article  MathSciNet  Google Scholar 

  20. Ghorbal, K., Goubault, E., Putot, S.: The zonotope abstract domain taylor1+. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 627–633. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  21. Gopan, D., Reps, T.: Lookahead widening. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 452–466. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  22. Halbwachs, N., Henry, J.: When the decreasing sequence fails. In: Miné, A., Schmidt, D. (eds.) SAS 2012. LNCS, vol. 7460, pp. 198–213. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  23. Jeannet, B.: Some experience on the software engineering of abstract interpretation tools. Electr. Notes Theor. Comput. Sci. (2) (2010)

    Google Scholar 

  24. Miné, A.: The octagon abstract domain. In: AST 2001 in WCRE 2001. IEEE (October 2001)

    Google Scholar 

  25. Monniaux, D.: Compositional analysis of floating-point linear numerical filters. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 199–212. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  26. Roux, P., Jobredeaux, R., Garoche, P.-L., Féron, É.: A generic ellipsoid abstract domain for linear time invariant systems. In: HSCC. ACM (2012)

    Google Scholar 

  27. Rump, S.M.: Verification of positive definiteness. BIT Numerical Mathematics 46 (2006)

    Article  MathSciNet  Google Scholar 

  28. Schrammel, P., Jeannet, B.: Logico-numerical abstract acceleration and application to the verification of data-flow programs. In: Yahav, E. (ed.) SAS 2011. LNCS, vol. 6887, pp. 233–248. Springer, Heidelberg (2011)

    Google Scholar 

  29. Seladji, Y., Bouissou, O.: Numerical abstract domain using support functions. In: Brat, G., Rungta, N., Venet, A. (eds.) NFM 2013. LNCS, vol. 7871, pp. 155–169. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  30. Sotin, P., Jeannet, B., Védrine, F., Goubault, E.: Policy iteration within logico-numerical abstract domains. In: Bultan, T., Hsiung, P.-A. (eds.) ATVA 2011. LNCS, vol. 6996, pp. 290–305. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. ONERA – The French Aerospace Lab, Toulouse, France

    Pierre Roux & Pierre-Loïc Garoche

  2. ISAE, University of Toulouse, Toulouse, France

    Pierre Roux

Authors
  1. Pierre Roux
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pierre-Loïc Garoche
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of Engineering and Technology, Vietnam National University, Xuan Thuy Street, 144, Hanoi, Vietnam

    Dang Van Hung

  2. School of Information Science, Japan Advanced Institute of Science and Technology, 1-1 Asahidai, 923-1292, Nomi, Ishikawa, Japan

    Mizuhito Ogawa

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer International Publishing Switzerland

About this paper

Cite this paper

Roux, P., Garoche, PL. (2013). Integrating Policy Iterations in Abstract Interpreters. In: Van Hung, D., Ogawa, M. (eds) Automated Technology for Verification and Analysis. Lecture Notes in Computer Science, vol 8172. Springer, Cham. https://doi.org/10.1007/978-3-319-02444-8_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-02444-8_18

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-02443-1

  • Online ISBN: 978-3-319-02444-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation