Bound Analysis of Imperative Programs with the Size-Change Abstraction

  • Florian Zuleger
  • Sumit Gulwani
  • Moritz Sinn
  • Helmut Veith
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6887)


The size-change abstraction (SCA) is an important program abstraction for termination analysis, which has been successfully implemented in many tools for functional and logic programs. In this paper, we demonstrate that SCA is also a highly effective abstract domain for the bound analysis of imperative programs.

We have implemented a bound analysis tool based on SCA for imperative programs. We abstract programs in a pathwise and context dependent manner, which enables our tool to analyze real-world programs effectively. Our work shows that SCA captures many of the essential ideas of previous termination and bound analysis and goes beyond in a conceptually simpler framework.


Transition System Transition Relation Nest Loop Disjunctive Normal Form 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.
  2. 2.
  3. 3.
    Ben-Amram, A.M.: Monotonicity constraints for termination in the integer domain. Technical report (2011)Google Scholar
  4. 4.
    Berdine, J., Chawdhary, A., Cook, B., Distefano, D., O’Hearn, P.W.: Variance analyses from invariance analyses. In: POPL, pp. 211–224 (2007)Google Scholar
  5. 5.
    Beyer, D., Cimatti, A., Griggio, A., Keremoglu, M.E., Sebastiani, R.: Software model checking via large-block encoding. In: FMCAD, pp. 25–32 (2009)Google Scholar
  6. 6.
    Colby, C., Lee, P.: Trace-based program analysis. In: POPL, pp. 195–207 (1996)Google Scholar
  7. 7.
    Cook, B., Podelski, A., Rybalchenko, A.: Termination proofs for systems code. In: PLDI, pp. 415–426 (2006)Google Scholar
  8. 8.
    Dutertre, B., de Moura, L.: The yices smt solver. Technical report (2006)Google Scholar
  9. 9.
    Goldsmith, S., Aiken, A., Wilkerson, D.S.: Measuring empirical computational complexity. In: ESEC/SIGSOFT FSE, pp. 395–404 (2007)Google Scholar
  10. 10.
    Gopan, D., Reps, T.W.: Lookahead widening. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 452–466. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  11. 11.
    Gulavani, B.S., Gulwani, S.: A numerical abstract domain based on expression abstraction and max operator with application in timing analysis. In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol. 5123, pp. 370–384. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  12. 12.
    Gulwani, S.: SPEED: Symbolic complexity bound analysis. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 51–62. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  13. 13.
    Gulwani, S., Jain, S., Koskinen, E.: Control-flow refinement and progress invariants for bound analysis. In: PLDI, pp. 375–385 (2009)Google Scholar
  14. 14.
    Gulwani, S., Mehra, K.K., Chilimbi, T.M.: Speed: precise and efficient static estimation of program computational complexity. In: POPL, pp. 127–139 (2009)Google Scholar
  15. 15.
    Gulwani, S., Zuleger, F.: The reachability-bound problem. In: PLDI, pp. 292–304 (2010)Google Scholar
  16. 16.
    Heizmann, M., Jones, N.D., Podelski, A.: Size-change termination and transition invariants. In: Cousot, R., Martel, M. (eds.) SAS 2010. LNCS, vol. 6337, pp. 22–50. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  17. 17.
    Krauss, A.: Certified size-change termination. In: Pfenning, F. (ed.) CADE 2007. LNCS (LNAI), vol. 4603, pp. 460–475. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  18. 18.
    Kroening, D., Sharygina, N., Tsitovich, A., Wintersteiger, C.M.: Termination analysis with compositional transition invariants. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 89–103. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  19. 19.
    Lattner, C., Adve, V.: Llvm: A compilation framework for lifelong program analysis & transformation. In: CGO 2004: Proceedings of the International Symposium on Code Generation and Optimization, p. 75. IEEE Computer Society, Washington, DC, USA (2004)Google Scholar
  20. 20.
    Lee, C.S., Jones, N.D., Ben-Amram, A.M.: The size-change principle for program termination. In: POPL, pp. 81–92 (2001)Google Scholar
  21. 21.
    Manolios, P., Vroon, D.: Termination analysis with calling context graphs. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 401–414. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  22. 22.
    Monniaux, D.: Automatic modular abstractions for linear constraints. In: POPL, pp. 140–151 (2009)Google Scholar
  23. 23.
    Podelski, A., Rybalchenko, A.: Transition invariants. In: LICS, pp. 32–41 (2004)Google Scholar
  24. 24.
    Podelski, A., Rybalchenko, A.: Transition predicate abstraction and fair termination. In: POPL, pp. 132–144 (2005)Google Scholar
  25. 25.
    Popeea, C., Chin, W.-N.: Inferring disjunctive postconditions. In: Okada, M., Satoh, I. (eds.) ASIAN 2006. LNCS, vol. 4435, pp. 331–345. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  26. 26.
    Tsitovich, A., Sharygina, N., Wintersteiger, C.M., Kroening, D.: Loop summarization and termination analysis. In: Abdulla, P.A., Leino, K.R.M. (eds.) TACAS 2011. LNCS, vol. 6605, pp. 81–95. Springer, Heidelberg (2011)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Florian Zuleger
    • 1
  • Sumit Gulwani
    • 2
  • Moritz Sinn
    • 1
  • Helmut Veith
    • 1
  1. 1.TU WienAustria
  2. 2.Microsoft ResearchUSA

Personalised recommendations