Succinct Representations for Abstract Interpretation

Combined Analysis Algorithms and Experimental Evaluation
  • Julien Henry
  • David Monniaux
  • Matthieu Moy
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7460)


Abstract interpretation techniques can be made more precise by distinguishing paths inside loops, at the expense of possibly exponential complexity. SMT-solving techniques and sparse representations of paths and sets of paths avoid this pitfall.

We improve previously proposed techniques for guided static analysis and the generation of disjunctive invariants by combining them with techniques for succinct representations of paths and symbolic representations for transitions based on static single assignment.

Because of the non-monotonicity of the results of abstract interpretation with widening operators, it is difficult to conclude that some abstraction is more precise than another based on theoretical local precision results. We thus conducted extensive comparisons between our new techniques and previous ones, on a variety of open-source packages.


Convex Polyhedron Abstract Interpretation Feasible Path Binary Decision Diagram Abstract Domain 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bagnara, R., Hill, P.M., Ricci, E., Zaffanella, E.: Precise widening operators for convex polyhedra. Science of Computer Programming 58(1-2), 28–56 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Bagnara, R., Hill, P.M., Zaffanella, E.: The Parma Polyhedra Library, version 0.9,
  3. 3.
    Bagnara, R., Hill, P.M., Zaffanella, E.: Widening operators for powerset domains. International Journal on Software Tools for Technology Transfer (STTT) 8(4-5), 449–466 (2006)CrossRefGoogle Scholar
  4. 4.
    Bagnara, R., Hill, P.M., Zaffanella, E.: The Parma Polyhedra Library: Toward a complete set of numerical abstractions for the analysis and verification of hardware and software systems. Science of Computer Programming 72(1-2), 3–21 (2008)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Balakrishnan, G., Sankaranarayanan, S., Ivancic, F., Gupta, A.: Refining the control structure of loops using static analysis. In: EMSOFT, pp. 49–58. ACM (2009)Google Scholar
  6. 6.
    Biere, A., Heule, M., van Maaren, H., Walsh, T. (eds.): Handbook of satisfiability. Frontiers in Artificial Intelligence and Applications, vol. 185. IOS Press, Amsterdam (2009)zbMATHGoogle Scholar
  7. 7.
    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: Programming Language Design and Implementation (PLDI), pp. 196–207. ACM (2003)Google Scholar
  8. 8.
    Cousot, P., Cousot, R.: Abstract interpretation frameworks. J. of Logic and Computation, 511–547 (August 1992)Google Scholar
  9. 9.
    Cousot, P., Cousot, R., Feret, J., Mauborgne, L., Miné, A., Monniaux, D., Rival, X.: The ASTREÉ Analyzer. In: Sagiv, M. (ed.) ESOP 2005. LNCS, vol. 3444, pp. 21–30. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  10. 10.
    Cousot, P., Halbwachs, N.: Automatic discovery of linear restraints among variables of a program. In: Principles of Programming Languages (POPL), pp. 84–96. ACM (1978)Google Scholar
  11. 11.
    Dutertre, B., de Moura, L.: A Fast Linear-Arithmetic Solver for DPLL(T). In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 81–94. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  12. 12.
    Gawlitza, T., Monniaux, D.: Improving Strategies via SMT Solving. In: Barthe, G. (ed.) ESOP 2011. LNCS, vol. 6602, pp. 236–255. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  13. 13.
    Gonnord, L., Halbwachs, N.: Combining Widening and Acceleration in Linear Relation Analysis. In: Yi, K. (ed.) SAS 2006. LNCS, vol. 4134, pp. 144–160. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  14. 14.
    Gopan, D., Reps, T.W.: Guided Static Analysis. In: Riis Nielson, H., Filé, G. (eds.) SAS 2007. LNCS, vol. 4634, pp. 349–365. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  15. 15.
    Gulwani, S., Zuleger, F.: The reachability-bound problem. In: PLDI, pp. 292–304. ACM (2010)Google Scholar
  16. 16.
    Halbwachs, N.: Détermination automatique de relations linéaires vérifiées par les variables d’un programme. Ph.D. thesis, Grenoble University (1979)Google Scholar
  17. 17.
    Halbwachs, N., Proy, Y.E., Roumanoff, P.: Verification of real-time systems using linear relation analysis. Formal Methods in System Design 11(2), 157–185 (1997)CrossRefGoogle Scholar
  18. 18.
    Harris, W.R., Sankaranarayanan, S., Ivancic, F., Gupta, A.: Program analysis via satisfiability modulo path programs. In: POPL, pp. 71–82. ACM (2010)Google Scholar
  19. 19.
    Henry, J.: Static Analysis by Path Focusing. Master’s thesis, Grenoble INP (2011),
  20. 20.
    Jeannet, B.: Dynamic partitioning in linear relation analysis: Application to the verification of reactive systems. Formal Methods in System Design 23(1), 5–37 (2003)zbMATHCrossRefGoogle Scholar
  21. 21.
    Jeannet, B., Miné, A.: Apron: A Library of Numerical Abstract Domains for Static Analysis. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 661–667. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  22. 22.
    Kroening, D., Strichman, O.: Decision procedures. Springer (2008)Google Scholar
  23. 23.
    Lattner, C., Adve, V.: LLVM: A compilation framework for lifelong program analysis & transformation. In: CGO, pp. 75–86. IEEE Computer Society, Washington, DC (2004)Google Scholar
  24. 24.
    LLVM team: LLVM Language Reference Manual (2011),
  25. 25.
    Miné, A.: The octagon abstract domain. Higher-Order and Symbolic Computation 19(1), 31–100 (2006)zbMATHCrossRefGoogle Scholar
  26. 26.
    Monniaux, D., Bodin, M.: Modular Abstractions of Reactive Nodes Using Disjunctive Invariants. In: Yang, H. (ed.) APLAS 2011. LNCS, vol. 7078, pp. 19–33. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  27. 27.
    Monniaux, D., Gonnord, L.: Using Bounded Model Checking to Focus Fixpoint Iterations. In: Yahav, E. (ed.) SAS 2011. LNCS, vol. 6887, pp. 369–385. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  28. 28.
    de Moura, L., Bjørner, N.: Z3: An Efficient SMT Solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  29. 29.
    Rival, X., Mauborgne, L.: The trace partitioning abstract domain. Transactions on Programming Languages and Systems (TOPLAS) 29(5), 26 (2007)CrossRefGoogle Scholar
  30. 30.
    Sharma, R., Dillig, I., Dillig, T., Aiken, A.: Simplifying Loop Invariant Generation Using Splitter Predicates. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 703–719. Springer, Heidelberg (2011)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Julien Henry
    • 1
    • 2
  • David Monniaux
    • 1
    • 3
  • Matthieu Moy
    • 1
    • 4
  1. 1.VERIMAG laboratoryGrenobleFrance
  2. 2.Université Joseph FourierFrance
  3. 3.CNRSFrance
  4. 4.Grenoble-INPFrance

Personalised recommendations