Automatic Complexity Analysis

  • Flemming Nielson
  • Hanne Riis Nielson
  • Helmut Seidl
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2305)

Abstract

We consider the problem of automating the derivation of tight asymptotic complexity bounds for solving Horn clauses. Clearly, the solving time crucially depends on the “sparseness” of the computed relations. Therefore, our asymptotic runtime analysis is accompanied by an asymptotic sparsity calculus together with an asymptotic sparsity analysis. The technical problem here is that least fixpoint iteration fails on asymptotic complexity expressions: the intuitive reason is that O(1)+ srO(1) = O(1) but O(1) + ⋯ + O(1) may return any value.

Keywords

Program analysis Horn clauses automatic complexity analysis sparseness 

References

  1. 1.
    A. Aiken. Introduction to set constraint-based program analysis. Science of Computer Programming (SCP), 35(2):79–111, 1999.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    D.A. Basin and H. Ganzinger. Complexity Analysis Based on Ordered Resolution. In 11th IEEE Symposium on Logic in Computer Science (LICS), 456–465, 1996. Long version to appear in JACM.Google Scholar
  3. 3.
    L. Cardelli and A.D. Gordon. Mobile ambients. In Proceedings of FoSSaCS’98, volume 1378 of LNCS, 140–155. Springer-Verlag, 1998.Google Scholar
  4. 4.
    E. Dahlhaus. Skolem normal forms concerning the least fixpoint. In Computation Theory and Logic, 101–106. LNCS 270, Springer Verlag, 1987.Google Scholar
  5. 5.
    D. L. Dill. Timing assumptions and verification of finite state concurrent systems. In Automatic Verification Methods for Finite State Systems, 197–212. LNCS 407, Springer Verlag, 1989.Google Scholar
  6. 6.
    C. Fecht and H. Seidl. A faster solver for general systems of equations. Science of Computer Programming (SCP), 35(2–3):137–162, 1999.MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    H. Ganzinger and D.A. McAllester. A new meta-complexity theorem for bottom-up logic programs. In First Int. Joint Conference on Automated Reasoning (IJCAR), 514–528. LNCS 2083, Springer Verlag, 2001.Google Scholar
  8. 8.
    G. Gottlob, E. Grädel, and H. Veith. Datalog LITE: A deductive query language with linear time model checking. ACM Transactions on Computational Logic, 2001. To appear.Google Scholar
  9. 9.
    D. E. Knuth. On a generalization of Dijkstra’s algorithm. Information Processing Letters (IPL), 6(1):1–5, 1977.MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    P.G. Kolaitis. Implicit definability on finite structures and unambiguous computations (preliminary report). In 5th Annual IEEE Symposium on Logic in Computer Science (LICS), 168–180, 1990.Google Scholar
  11. 11.
    D. McAllester. On the complexity analysis of static analyses. In 6th Static Analysis Symposium (SAS), 312–329. LNCS 1694, Springer Verlag, 1999.CrossRefGoogle Scholar
  12. 12.
    F. Nielson and H. Seidl. Control-flow analysis in cubic time. In European Symposium on Programming (ESOP), 252–268. LNCS 2028, Springer Verlag, 2001.Google Scholar
  13. 13.
    F. Nielson and H. Seidl. Succinct solvers. Technical Report 01-12, University of Trier, Germany, 2001.Google Scholar
  14. 14.
    R. Shaham, K. Kordner, and S. Sagiv. Automatic removal of array memory leaks in Java. In Compiler Construction (CC), 50–66. LNCS 1781, Springer Verlag, 2000.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Flemming Nielson
    • 1
  • Hanne Riis Nielson
    • 1
  • Helmut Seidl
    • 2
  1. 1.Informatics and Mathematical ModellingThe Technical University of DenmarkKongens LyngbyDenmark
  2. 2.Fachbereich IV — InformatikUniversität TrierTrierGermany

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