On the Limits of the Classical Approach to Cost Analysis

  • Diego Esteban Alonso-Blas
  • Samir Genaim
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7460)

Abstract

The classical approach to static cost analysis is based on transforming a given program into cost relations and solving them into closed-form upper-bounds. It is known that for some programs, this approach infers upper-bounds that are asymptotically less precise than the actual cost. As yet, it was assumed that this imprecision is due to the way cost relations are solved into upper-bounds. In this paper: (1) we show that this assumption is partially true, and identify the reason due to which cost relations cannot precisely model the cost of such programs; and (2) to overcome this imprecision, we develop a new approach to cost analysis, based on SMT and quantifier elimination. Interestingly, we find a strong relation between our approach and amortised cost analysis.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Albert, E., Arenas, P., Genaim, S., Puebla, G.: Closed-Form Upper Bounds in Static Cost Analysis. Journal of Automated Reasoning 46(2), 161–203 (2011)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Albert, E., Arenas, P., Genaim, S., Puebla, G., Zanardini, D.: Cost Analysis of Object-Oriented Bytecode Programs. Theoretical Computer Science 413(1), 142–159 (2012)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Albert, E., Genaim, S., Gómez-Zamalloa, M.: Parametric Inference of Memory Requirements for Garbage Collected Languages. In: ISMM, pp. 121–130. ACM, New York (2010)Google Scholar
  4. 4.
    Albert, E., Genaim, S., Masud, A.N.: More Precise Yet Widely Applicable Cost Analysis. In: Jhala, R., Schmidt, D. (eds.) VMCAI 2011. LNCS, vol. 6538, pp. 38–53. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  5. 5.
    Anderson, H., Khoo, S.-C., Andrei, Ş., Luca, B.: Calculating Polynomial Runtime Properties. In: Yi, K. (ed.) APLAS 2005. LNCS, vol. 3780, pp. 230–246. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  6. 6.
    Benoy, F., King, A.: Inferring Argument Size Relationships with CLP(R). In: Gallagher, J.P. (ed.) LOPSTR 1996. LNCS, vol. 1207, pp. 204–223. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  7. 7.
    Brown, C.W., Gross, C.: Efficient Preprocessing Methods for Quantifier Elimination. In: Ganzha, V.G., Mayr, E.W., Vorozhtsov, E.V. (eds.) CASC 2006. LNCS, vol. 4194, pp. 89–100. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  8. 8.
    Chen, Y., Xia, B., Yang, L., Zhan, N., Zhou, C.: Discovering Non-linear Ranking Functions by Solving Semi-algebraic Systems. In: Jones, C.B., Liu, Z., Woodcock, J. (eds.) ICTAC 2007. LNCS, vol. 4711, pp. 34–49. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  9. 9.
    Cormen, T.H., Leiserson, C.E., Rivest, R., Stein, C.: Introduction to Algorithms, 3rd edn. MIT Press (2009)Google Scholar
  10. 10.
    Debray, S.K., Lin, N.-W.: Cost Analysis of Logic Programs. ACM Transactions on Programming Languages and Systems 15(5), 826–875 (1993)CrossRefGoogle Scholar
  11. 11.
    Dolzmann, A., Sturm, T.: REDLOG: Computer Algebra meets Computer Logic. ACM SIGSAM Bulletin 31(2), 2–9 (1997)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Gulwani, S., Mehra, K.K., Chilimbi, T.M.: SPEED: Precise and Efficient Static Estimation of Program Computational Complexity. In: Proc. of POPL 2009, pp. 127–139. ACM (2009)Google Scholar
  13. 13.
    Gulwani, S., Zuleger, F.: The Reachability-Bound Problem. In: PLDI, pp. 292–304. ACM (2010)Google Scholar
  14. 14.
    Hickey, T.J., Cohen, J.: Automating Program Analysis. J. ACM 35(1), 185–220 (1988)MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Hofmann, M., Hoffmann, J., Aehlig, K.: Multivariate Amortized Resource Analysis. In: POPL 2011, pp. 357–370. ACM (2011)Google Scholar
  16. 16.
    Kapur, D.: Automatically generating loop invariants using quantifier elimination. In: Deduction and Applications, vol. 05431 (2006)Google Scholar
  17. 17.
    Le Métayer, D.: ACE: An Automatic Complexity Evaluator. ACM Trans. Program. Lang. Syst. 10(2), 248–266 (1988)CrossRefGoogle Scholar
  18. 18.
    Monniaux, D.: Automatic modular abstractions for template numerical constraints. Logical Methods in Computer Science 6(3) (2010)Google Scholar
  19. 19.
    Sturm, T., Tiwari, A.: Verification and Synthesis using Real Quantifier Elimination. In: ISSAC 2011, pp. 329–336. ACM (2011)Google Scholar
  20. 20.
    REDUCE Computer Algebra System. REDUCE home pageGoogle Scholar
  21. 21.
    Z3 Theorem Prover. Z3 home pageGoogle Scholar
  22. 22.
    Wegbreit, B.: Mechanical Program Analysis. Communications of the ACM 18(9) (1975)Google Scholar
  23. 23.
    Zuleger, F., Gulwani, S., Sinn, M., Veith, H.: Bound Analysis of Imperative Programs with the Size-Change Abstraction. In: Yahav, E. (ed.) SAS 2011. LNCS, vol. 6887, pp. 280–297. Springer, Heidelberg (2011)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Diego Esteban Alonso-Blas
    • 1
  • Samir Genaim
    • 1
  1. 1.DSICComplutense University of Madrid (UCM)Spain

Personalised recommendations