Skip to main content

On the Complexity Analysis of Static Analyses

  • Conference paper
  • First Online:
Static Analysis (SAS 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1694))

Included in the following conference series:

Abstract

This paper investigates bottom-up logic programming as a formalism for expressing static analyses. The main technical contribution consists of two meta-complexity theorems which allow, in many cases, the asymptotic running time of a bottom-up logic program to be determined by inspection. It is well known that a datalog program runs in O(n k) time where k is the largest number of free variables in any single rule. The theorems given here are significantly more refined. A variety of algorithms given as bottom-up logic programs are analyzed as examples.

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 54.99
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. A. Aiken, E. Wimmers, and T.K. Lakshman. Soft typing with conditional types. In ACM Symposium on Principles of Programming Languages, pages 163–173. Association for Computing Machinery, 1994.

    Google Scholar 

  2. David Basin and Herald Ganzinger. Automated complexity analysis based on ordered resolution. In Proceedings, Eleventh Annual IEEE Symposium on Logic in Computer Science, pages 456–465. IEEE Computer Society Press, 1996.

    Google Scholar 

  3. A. Bondorf and A. Jorgensen. Efficient analysis for realistic off-line partial evaluation. Journal of functional Programming, 3(3), 1993.

    Google Scholar 

  4. Keith L. Clark. Logic programming schemes and their implementations. In Jean-Louis Lassez and Gordon Plotkin, editors, Computational Logic. MIT Press, 1991.

    Google Scholar 

  5. William Downing and Jean H. Gallier. Linear time algorithms for testing the satisfiability of propositional horn formulae. Journal of Logic Programming, 1(3):267–284, 1984.

    Article  MathSciNet  Google Scholar 

  6. Manual Fähndrich, Jeffery Foster, Zhendong Su, and Alexander Aiken. Partial online cycle elimination in inclusion constraint graphs. In PLDI98, 1998.

    Google Scholar 

  7. Robert Givan and David McAllester. New results on local inference relations. In Principles of Knowlwedge Representation and Reasoning: Proceedings of the Third International Conference, pages 403–412. Morgan Kaufman Press, October 1992. internet file ftp://ftp.ai.mit.edu:/pub/users/dam/kr92.ps.

  8. N. Heintze. Set based analysis of ml programs. In ACM Conference on Lisp and Functional Programming, pages 306–317, 1994.

    Google Scholar 

  9. Nevin Heintze and David McAllester. Linear time subtransitive control flow analysis. In PLDI-97, 1997.

    Google Scholar 

  10. Nevin Heintze and David McAllester. On the cubic bottleneck in subtyping and flow analysis. In Proceedings, Twelvth Annual IEEE Symposium on Logic in Computer Science, pages 342–361. IEEE Computer Society Press, 1997.

    Google Scholar 

  11. Fritz Henglein. Breaking through the n 3 barrier: Faster object type inference. Theory and Practice of Object Systems (TAPOS), 5(1):57–72, 1999. A Preliminary Version appeared in FOOL4.

    Article  Google Scholar 

  12. R. A. Kowalski. Predicate logic as a programming language. In IFIP 74, 1974.

    Google Scholar 

  13. Dexter Kozen, Jens Palsberg, and Michael I. Schwartzbach. Efficient inference of partial types. J. Comput. Syst. Sci., 49(2):306–324, October 1994.

    Article  MATH  MathSciNet  Google Scholar 

  14. D. McAllester. Automatic recognition of tractability in inference relations. JACM, 40(2):284–303, April 1993. internet file ftp://ftp.ai.mit.edu:/pub/users/dam/jacm2.ps.

    Article  MATH  MathSciNet  Google Scholar 

  15. David McAllester. Inferring recursive types. Available at http://www.research.mit.edu/~dmac, 1996.

  16. E. Melski and T. Reps. Intercovertability of set constraints and context free language reachability. In PEPM’97, 1997.

    Google Scholar 

  17. Jeff Naughton and Raghu Ramakrishnan. Bottom-up evaluation of logic programs. In Jean-Louis Lassez and Gordon Plotkin, editors, Computational Logic. MIT Press, 1991.

    Google Scholar 

  18. J. Palsberg. Efficient inference of object types. Information and Computation, 123(2):198–209, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  19. J. Palsberg and P. O’Keefe. A type system equivalent to flow analysis. In POPL95, pages 367–378, 1995.

    Google Scholar 

  20. M. S. Paterson and M. N. Wegman. Linear unification. JCSS, 16:158–167, 1978.

    MATH  MathSciNet  Google Scholar 

  21. J. Ullman. Bottom-up beats top-down for datalog. In Proceedings of the Eigth ACM SIGACT-SIGMOD-SIGART Symposium on the Principles of Database Systems, pages 140–149, March 1989.

    Google Scholar 

  22. M. Vardi. Complexity of relational query languages. In 14th Symposium on Theory of Computation, pages 137–146, 1982.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

McAllester, D. (1999). On the Complexity Analysis of Static Analyses. In: Cortesi, A., Filé, G. (eds) Static Analysis. SAS 1999. Lecture Notes in Computer Science, vol 1694. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48294-6_21

Download citation

  • DOI: https://doi.org/10.1007/3-540-48294-6_21

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66459-8

  • Online ISBN: 978-3-540-48294-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics