Skip to main content
View expanded cover

International Conference on Verification, Model Checking, and Abstract Interpretation

VMCAI 2018: Verification, Model Checking, and Abstract Interpretation pp 205–225Cite as

From Shapes to Amortized Complexity

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 10747)

Abstract

We propose a new method for the automated resource bound analysis of programs manipulating dynamic data structures built on top of an underlying shape and resource bound analysis. Our approach first constructs an integer abstraction for the input program using information gathered by a shape analyser; then a resource bound analyzer is run on the resulting integer program. The integer abstraction is based on shape norms — numerical measures on dynamic data structures (e.g., the length of a linked list). In comparison to related approaches, we consider a larger class of shape norms which we derive by a lightweight program analysis. The analysis identifies paths through the involved dynamic data structures, and filters the norms which are unlikely to be useful for the later bound analysis. We present a calculus for deriving the numeric changes of the shape norms, thereby generating the integer program. Our calculus encapsulates the minimal information which is required from the shape analysis.

We have implemented our approach on top of the Forester shape analyser and evaluated it on a number of programs manipulating various list and tree structures using the Loopus tool as the underlying bounds analyser. We report on programs with complex data structures and/or using complex algorithms that could not be analysed in a fully automated and precise way before.

Supported by the Czech Science Foundation (project 17-12465S), the BUT FIT project FIT-S-17-4014, the IT4IXS: IT4Innovations Excellence in Science project (LQ1602) and the Austrian National Research Network S11403-N23 (RiSE) of the Austrian Science Fund (FWF).

This is a preview of subscription content, access via your institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-319-73721-8_10
  • Chapter length: 21 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   84.99
Price excludes VAT (USA)
  • ISBN: 978-3-319-73721-8
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   107.00
Price excludes VAT (USA)
Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Sinn, M., Zuleger, F., Veith, H.: Complexity and resource bound analysis of imperative programs using difference constraints. J. Autom. Reasoning 59(1), 3–45 (2017)

    MathSciNet  CrossRef  MATH  Google Scholar 

  2. Gulwani, S., Lev-Ami, T., Sagiv, M.: A combination framework for tracking partition sizes. In: Proc. of POPL 2009, pp. 239–251 (2009)

    Google Scholar 

  3. Hofmann, M., Rodriguez, D.: Automatic type inference for amortised heap-space analysis. In: Felleisen, M., Gardner, P. (eds.) ESOP 2013. LNCS, vol. 7792, pp. 593–613. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-37036-6_32

    CrossRef  Google Scholar 

  4. Atkey, R.: Amortised resource analysis with separation logic. Logical Methods in Computer Science 7(2) (2011)

    Google Scholar 

  5. Albert, E., Arenas, P., Genaim, S., Gómez-Zamalloa, M., Puebla, G.: Automatic inference of resource consumption bounds. In: Bjørner, N., Voronkov, A. (eds.) LPAR 2012. LNCS, vol. 7180, pp. 1–11. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-28717-6_1

    CrossRef  Google Scholar 

  6. Frohn, F., Giesl, J.: Complexity analysis for Java with AProVE. In: Polikarpova, N., Schneider, S. (eds.) IFM 2017. LNCS, vol. 10510, pp. 85–101. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-66845-1_6

    CrossRef  Google Scholar 

  7. Holík, L., Hruška, M., Lengál, O., Rogalewicz, A., Šimáček, J., Vojnar, T.: Forester: shape analysis using tree automata (competition contribution). In: Baier, C., Tinelli, C. (eds.) TACAS 2015. LNCS, vol. 9035, pp. 432–435. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46681-0_37

    Google Scholar 

  8. Sinn, M., Zuleger, F.: Loopus - a tool for computing loop bounds for c programs. In: Proc. of WING@ETAPS/IJCAR (2010)

    Google Scholar 

  9. Ströder, T., Aschermann, C., Frohn, F., Hensel, J., Giesl, J.: AProVE: termination and memory safety of C programs (competition contribution). In: Baier, C., Tinelli, C. (eds.) TACAS 2015. LNCS, vol. 9035, pp. 417–419. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46681-0_32

    Google Scholar 

  10. Bouajjani, A., Bozga, M., Habermehl, P., Iosif, R., Moro, P., Vojnar, T.: Programs with Lists are Counter Automata. Formal Methods in System Design 38(2) (2011)

    Google Scholar 

  11. Berdine, J., Cook, B., Distefano, D., O’Hearn, P.W.: Automatic termination proofs for programs with shape-shifting heaps. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 386–400. Springer, Heidelberg (2006). https://doi.org/10.1007/11817963_35

    CrossRef  Google Scholar 

  12. Lahiri, S., Qadeer, S.: Verifying properties of well-founded linked lists. In: Proc. of POPL 2006. ACM Press (2006)

    Google Scholar 

  13. Yavuz-Kahveci, T., Bultan, T.: Automated verification of concurrent linked lists with counters. In: Hermenegildo, M.V., Puebla, G. (eds.) SAS 2002. LNCS, vol. 2477, pp. 69–84. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-45789-5_8

    CrossRef  Google Scholar 

  14. Berdine, J., Chawdhary, A., Cook, B., Distefano, D., O’Hearn, P.: Variance analyses from invariance analyses. In: Proc. of POPL 2007. ACM (2007)

    Google Scholar 

  15. Rugina, R.: Quantitative shape analysis. In: Giacobazzi, R. (ed.) SAS 2004. LNCS, vol. 3148, pp. 228–245. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-27864-1_18

    CrossRef  Google Scholar 

  16. Habermehl, P., Iosif, R., Rogalewicz, A., Vojnar, T.: Proving termination of tree manipulating programs. In: Namjoshi, K.S., Yoneda, T., Higashino, T., Okamura, Y. (eds.) ATVA 2007. LNCS, vol. 4762, pp. 145–161. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-75596-8_12

    CrossRef  Google Scholar 

  17. Magill, S., Tsai, M.H., Lee, P., Tsay, Y.K.: Automatic numeric abstractions for heap-manipulating programs. In: Proc. of POPL 2010 (2010)

    Google Scholar 

  18. Magill, S., Tsai, M.-H., Lee, P., Tsay, Y.-K.: THOR: a tool for reasoning about shape and arithmetic. In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol. 5123, pp. 428–432. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-70545-1_41

    CrossRef  Google Scholar 

  19. Sinn, M., Zuleger, F., Veith, H.: A simple and scalable static analysis for bound analysis and amortized complexity analysis. In: Biere, A., Bloem, R. (eds.) CAV 2014. LNCS, vol. 8559, pp. 745–761. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-08867-9_50

    Google Scholar 

  20. Bouajjani, A., Habermehl, P., Vojnar, T.: Abstract regular model checking. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 372–386. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-27813-9_29

    CrossRef  Google Scholar 

  21. Abdulla, P.A., Haziza, F., Holík, L., Jonsson, B., Rezine, A.: An integrated specification and verification technique for highly concurrent data structures. In: Piterman, N., Smolka, S.A. (eds.) TACAS 2013. LNCS, vol. 7795, pp. 324–338. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-36742-7_23

    CrossRef  Google Scholar 

  22. Holík, L., Hruška, M., Lengál, O., Rogalewicz, A., Vojnar, T.: Counterexample validation and interpolation-based refinement for forest automata. In: Bouajjani, A., Monniaux, D. (eds.) VMCAI 2017. LNCS, vol. 10145, pp. 288–309. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-52234-0_16

    CrossRef  Google Scholar 

  23. Holík, L., Lengál, O., Rogalewicz, A., Šimáček, J., Vojnar, T.: Fully automated shape analysis based on forest automata. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 740–755. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-39799-8_52

    CrossRef  Google Scholar 

  24. Bjørner, N.: The Z3 Theorem Prover. https://github.com/Z3Prover/z3/

Download references

Author information

Authors and Affiliations

  1. FIT, IT4Innovations Centre of Excellence, Brno University of Technology, Brno, Czech Republic

    Tomáš Fiedor, Lukáš Holík, Adam Rogalewicz & Tomáš Vojnar

  2. TU Wien, Vienna, Austria

    Florian Zuleger

  3. St. Pölten University of Applied Sciences, Sankt Pölten, Austria

    Moritz Sinn

Authors
  1. Tomáš Fiedor
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lukáš Holík
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Adam Rogalewicz
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Moritz Sinn
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Tomáš Vojnar
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Florian Zuleger
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tomáš Fiedor .

Editor information

Editors and Affiliations

  1. University of Texas , Austin, Texas, USA

    Isil Dillig

  2. University of California , Los Angeles, California, USA

    Dr. Jens Palsberg

Rights and permissions

Reprints and Permissions

Copyright information

© 2018 Springer International Publishing AG

About this paper

Verify currency and authenticity via CrossMark

Cite this paper

Fiedor, T., Holík, L., Rogalewicz, A., Sinn, M., Vojnar, T., Zuleger, F. (2018). From Shapes to Amortized Complexity. In: Dillig, I., Palsberg, J. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2018. Lecture Notes in Computer Science(), vol 10747. Springer, Cham. https://doi.org/10.1007/978-3-319-73721-8_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-73721-8_10

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-73720-1

  • Online ISBN: 978-3-319-73721-8

  • eBook Packages: Computer ScienceComputer Science (R0)