Skip to main content

Interpolation-Based Height Analysis for Improving a Recurrence Solver

  • Conference paper
Foundational and Practical Aspects of Resource Analysis (FOPARA 2011)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 7177))

Abstract

The COSTA system infers resource consumption bounds from Java bytecode using an internal recurrence solver PUBS. This paper suggests an improvement of the COSTA system, such that it can solve a larger number of recurrences. The idea is to replace one of its static analyses, the ranking function analysis, by another kind of analysis, height analysis, in such a way that polynomial bounds of any degree may be inferred instead of just linear expressions. The work can be seen as an application of some polynomial interpolation techniques used by some of the authors in prior analyses. Finding a way to choose proper test nodes is the key to the solution presented in this paper.

This work was partly funded by the EU Artemis Joint Undertaking in the CHARTER project, grant-nr. 100039, and by Spanish FPU grant AP2006-02154 and projects TIN2008-06622-C03-01 (STAMP), S2009/TIC-1465 (PROMETIDOS).

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 49.99
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. Albert, E., Arenas, P., Genaim, S., Puebla, G., Zanardini, D.: COSTA: Design and Implementation of a Cost and Termination Analyzer for Java Bytecode. In: de Boer, F.S., Bonsangue, M.M., Graf, S., de Roever, W.-P. (eds.) FMCO 2007. LNCS, vol. 5382, pp. 113–132. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  2. Albert, E., Arenas, P., Genaim, S., Puebla, G.: Closed-form upper bounds in static cost analysis. J. Autom. Reasoning 46(2), 161–203 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  3. Albert, E., Genaim, S., Gómez-Zamalloa, M.: Parametric inference of memory requirements for garbage collected languages. In: Vitek, J., Lea, D. (eds.) ISMM, pp. 121–130. ACM (2010)

    Google Scholar 

  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)

    Chapter  Google Scholar 

  5. Bagnara, R., Zaccagnini, A., Zolo, T.: The automatic solution of recurrence relations. I. Linear recurrences of finite order with constant coefficients. Quaderno 334, Dipartimento di Matematica, Università di Parma, Italy (2003), http://www.cs.unipr.it/Publications/

  6. Bagnara, R., Ricci, E., Zaffanella, E., Hill, P.M.: Possibly Not Closed Convex Polyhedra and the Parma Polyhedra Library. In: Hermenegildo, M.V., Puebla, G. (eds.) SAS 2002. LNCS, vol. 2477, pp. 213–229. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  7. Brown, C.W.: QEPCAD: Quantifier Elimination by Partial Cylindrical Algebraic Decomposition (2004), http://www.cs.usna.edu/qepcad/B/QEPCAD.html

  8. Chui, C.K., Lai, M.J.: Vandermonde determinants and lagrange interpolation in R s. In: Nonlinear and Convex Analysis, Proceedings in Honor of Ky Fan, pp. 23–35. Marcel Dekker Inc., N.Y. (1987)

    Google Scholar 

  9. Collins, G.E.: Quantifier Elimination for Real Closed Fields by Cylindrical Algebraic Decomposition. In: Brakhage, H. (ed.) GI-Fachtagung 1975. LNCS, vol. 33, pp. 134–183. Springer, Heidelberg (1975)

    Google Scholar 

  10. Cooper, D.C.: Theorem proving in arithmetic without multiplication. Machine Intelligence 7, 91–100 (1972)

    MATH  Google Scholar 

  11. Dolzmann, A., Sturm, T.: Redlog user manual. Tech. Rep. MIP-9905, FMI, Universität Passau, edition 2.0 for Version 2.0 (1999)

    Google Scholar 

  12. van Eekelen, M., Shkaravska, O., van Kesteren, R., Jacobs, B., Poll, E., Smetsers, S.: AHA: Amortized Heap space usage Analysis. In: Morazán, M. (ed.) Selected Revised Papers of the 8th International Symposium on Trends in Functional Programming (TFP 2007), pp. 36–53. Intellect, New York (2007)

    Google Scholar 

  13. Hearn, A.C.: REDUCE. User’s Manual. Version 3.8 (2004)

    Google Scholar 

  14. Hoffmann, J., Hofmann, M.: Amortized Resource Analysis with Polynomial Potential. In: Gordon, A.D. (ed.) ESOP 2010. LNCS, vol. 6012, pp. 287–306. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  15. Hoffmann, J., Aehlig, K., Hofmann, M.: Multivariate amortized resource analysis. In: Ball, T., Sagiv, M. (eds.) POPL, pp. 357–370. ACM (2011)

    Google Scholar 

  16. Hofmann, M., Jost, S.: Static prediction of heap space usage for first-order functional programs. In: Proc. 30th ACM Symp. on Principles of Programming Languages, POPL 2003, pp. 185–197. ACM Press (2003)

    Google Scholar 

  17. van Kesteren, R., Shkaravska, O., van Eekelen, M.: Inferring static non-monotonically sized types through testing. In: Proceedings of 16th International Workshop on Functional and (Constraint) Logic Programming (WFLP 2007), Paris, France. ENTCS, vol. 216C, pp. 45–63 (2007)

    Google Scholar 

  18. Lucas, S.: Polynomials over the reals in proofs of termination: from theory to practice. RAIRO Theoretical Informatics and Applications 39(3), 547–586 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  19. Nipkow, T.: Linear quantifier elimination. J. Autom. Reasoning 45(2), 189–212 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  20. Podelski, A., Rybalchenko, A.: A Complete Method for the Synthesis of Linear Ranking Functions. In: Steffen, B., Levi, G. (eds.) VMCAI 2004. LNCS, vol. 2937, pp. 239–251. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  21. Shkaravska, O., van Eekelen, M., van Kesteren, R.: Polynomial size analysis of first-order shapely functions. Logical Methods in Computer Science 5(2:10), 1–35 (2009); selected Papers from TLCA 2007

    Google Scholar 

  22. Shkaravska, O., van Eekelen, M., Tamalet, A.: Collected Size Semantics for Functional Programs over Lists. In: Scholz, S.-B., Chitil, O. (eds.) IFL 2008. LNCS, vol. 5836, pp. 118–137. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  23. Shkaravska, O., van Eekelen, M.C.J.D., van Kesteren, R.: Polynomial size analysis of first-order shapely functions. Logical Methods in Computer Science 5(2) (2009)

    Google Scholar 

  24. Shkaravska, O., Kersten, R., van Eekelen, M.: Test-based inference of polynomial loop-bound functions. In: Proceedings of the 8th International Conference on the Principles and Practice of Programming in Java, PPPJ 2010. ACM (2010)

    Google Scholar 

  25. Tamalet, A., Shkaravska, O., van Eekelen, M.: Size analysis of algebraic data types. In: Achten, P., Koopman, P., Morazán, M.T. (eds.) Selected Revised Papers of the 9th International Symposium on Trends in Functional Programming (TFP 2008), pp. 33–48. Intellect (2009)

    Google Scholar 

  26. Tarski, A.: A Decision Method for Elementary Algebra and Geometry. University of California Press, Berkeley (1948)

    MATH  Google Scholar 

  27. Wegbreit, B.: Mechanical program analysis. Commun. ACM 18(9), 528–539 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  28. Weispfenning, V.: The complexity of linear problems in fields. J. Symb. Comput. 5(1/2), 3–27 (1988)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Montenegro, M., Shkaravska, O., van Eekelen, M., Peña, R. (2012). Interpolation-Based Height Analysis for Improving a Recurrence Solver. In: Peña, R., van Eekelen, M., Shkaravska, O. (eds) Foundational and Practical Aspects of Resource Analysis. FOPARA 2011. Lecture Notes in Computer Science, vol 7177. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32495-6_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-32495-6_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32494-9

  • Online ISBN: 978-3-642-32495-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics