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Tailoring recursion for complexity

  • Erich Grädel
  • Yuri Gurevich
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 820)

Abstract

In this paper, a global function is a function that computes a (local) function in each ordered structure of a specified vocabulary. We design algebras of global functions for a number of complexity classes for which such algebras have not been known, e.g. for the functions computable in nondeterministic logarithmic space, or in nondeterministic polynomial time. In addition, we present a functional analogue of first-order logic and give a new functional characterization of polynomial time.

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References

  1. [1]
    S. Abiteboul and V. Vianu, Datalog Extensions for Database Queries and Updates, J. Computer and System Sciences 43 (1991), 62–124.Google Scholar
  2. [2]
    K. Compton and C. Laflamme, An Algebra and a Logic for NC 1, Information and Computation 87 (1990), 241–263.Google Scholar
  3. [3]
    R. Fagin, Generalized first-order spectra and polynomial-time recognizable sets, SIAM-AMS Proc. 7 (1974), 43–73.Google Scholar
  4. [4]
    A. Goerdt, Characterizing complexity classes by general recursive definitions in higher types, Proceedings of CSL '88, Lecture Notes in Computer Science Nr. 385, Springer (1989), 99–117.Google Scholar
  5. [5]
    E. Grädel, Capturing Complexity Classes by Fragments of Second Order Logic, Theoretical Computer Science 101 (1992), 35–57.Google Scholar
  6. [6]
    E. Grädel and M. Otto, Inductive Definability with Counting on Finite Structures, Proceedings of CSL92, Lecture Notes in Computer Science Nr. 702 (1993), 231–247.Google Scholar
  7. [7]
    Y. Gurevich, Algebras of feasible functions, Proceedings of 24th IEEE Symposium on Foundations of Computer Science 1983, 210–214.Google Scholar
  8. [8]
    Y. Gurevich, Toward logic tailord for computational complexity, Computation and Proof Theory, Lecture Notes in Mathematics Nr. 1104, Springer (1984), 175–216.Google Scholar
  9. [9]
    Y. Gurevich, Logic and the Challenge of Computer Science, in: E. Börger (Ed), Trends in Theoretical Computer Science, Computer Science Press (1988), 1–57.Google Scholar
  10. [10]
    Y. Gurevich and H. Lewis, A Logic for Constant-Depth Circuits, Information and Control 61 (1984), 65–74.Google Scholar
  11. [11]
    N. Immerman, Descriptive and Computational Complexity, Proc. of AMS Symposia in Appl. Math. 38 (1989), 75–91.Google Scholar
  12. [12]
    Libo Lo, Functions and Functionals on Finite Systems, Journal of Symbolic Logic 57 (1992), 118–130.Google Scholar
  13. [13]
    V. Sazonov, Polynomial computability and recursivity in finite domains, Elektronische Datenverarbeitung und Kybernetik 16 (1980), 319–323.Google Scholar
  14. [14]
    M. Vardi, Complexity of Relational Query Languages, Proc. of 14th Symposium on Theory of Computing (1982), 137–146.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Erich Grädel
    • 1
  • Yuri Gurevich
    • 2
  1. 1.Lehrgebiet Mathematische Grundlagen der InformatikRWTH AachenAachenGermany
  2. 2.EECS DepartmentUniversity of MichiganAnn ArborUSA

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