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Semantic analysis of interval congruences

  • François Masdupuy
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 735)

Abstract

This paper describes a new non relational semantic analysis of program integer variables. Interval congruence analysis is designed using Cousot's abstract interpretation framework, its model generalizes integer intervals and integer cosets by the definition of coset congruences. The use of a widening operator defined on rational approximations of the integer model ensures fast convergences of the iteration process whereas the diversity of patterns of the modeled integer sets increases the accuracy of the analysis.

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References

  1. [CC76]
    P. Cousot and R. Cousot. Static determination of dynamic properties of programs. In Paris Dunod, editor, Proc. of the second International Symposium on programming, pages 106–130, 1976.Google Scholar
  2. [CC77]
    P. Cousot and R. Cousot. Abstract interpretation: a unified lattice model for static analysis of programs by construction of approximation of fixpoints. In 4th Annual ACM Symposium on Principles of Programming Languages, pages 238–252, Los Angeles, January 1977.Google Scholar
  3. [CC79]
    P. Cousot and R. Cousot. Systematic design of program analysis frameworks. In 6th Annual ACM Symposium on Principles of Programming Languages, pages 269–282, 1979.Google Scholar
  4. [CC92a]
    P. Cousot and R. Cousot. Abstract interpretation and application to logic programs. Journal of Logic Programming, 13(2–3), 1992.Google Scholar
  5. [CC92b]
    P. Cousot and R. Cousot. Abstract interpretation frameworks. Journal of Logic and Computation, 1992.Google Scholar
  6. [CC92c]
    P. Cousot and R. Cousot. Comparing the galois connection and widening/narrowing approaches to abstract interpretation. Technical Report LIX/RR/92/09, Laboratoire d'Informatique de l'X, Ecole Polytechnique, 91128 Palaiseau cedex, France, 1992.Google Scholar
  7. [Gra89]
    P. Granger. Static analysis of arithmetical congruences. Intern. J. Computer Math., 30:165–190, 1989.Google Scholar
  8. [Gra91a]
    P. Granger. Analyses sémantiques de congruence. PhD thesis. Ecole Polytechnique, Palaiseau, July 1991.Google Scholar
  9. [Gra91b]
    P. Granger. Static analysis of linear congruence equalities among variables of a program. In International Joint Conference on Theory and Practice of Software Development, volume 493 of Lecture Notes on Computer Science, pages 169–192. Springer Verlag, 1991.Google Scholar
  10. [Mas92a]
    F. Masdupuy. Array operations abstraction using semantic analysis of trapezoid congruences. In International Conference on Supercomputing, July 1992.Google Scholar
  11. [Mas92b]
    F. Masdupuy. Semantic analysis of rational interval congruences. Research Report LIX/RR/92/05, Ecole Polytechnique, 91128 Palaiseau, 1992.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • François Masdupuy
    • 1
  1. 1.Centre de Recherche en InformatiqueÉcole des Mines de ParisFontainebleau cedexFrance

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