On logical descriptions of some concepts in structural complexity theory

  • Erich Grädel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 440)


A logical framework is introduced which captures the behaviour of oracle machines and gives logical descriptions of complexity classes that are defined by oracle machines. Using this technique the notion of first-order selfreducibility is investigated and applied to obtain a structural result about non-uniform complexity classes below P.


Complexity Theory Logical Description Order Logic Travel Salesperson Problem First Order 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    S. Buss and L. Hay, On truth-table reducibility to SAT and the difference hierarchy over NP, Proceedings of 3rd Conference on Structure in Complexity Theory 1988, 224–233.Google Scholar
  2. [2]
    J. Cai and L. Hemachandra, The Boolean hierarchy: hardware over NP, Proceedings of 1st Conference on Structure in Complexity Theory 1986, Lecture Notes in Computer Science Nr. 223, Springer 1986, 105–124.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]
    E. Grandjean, The Spectra of First-Order Sentences and Computational Complexity, SIAM J. Comp. 13 (1984), 367–373.Google Scholar
  5. [5]
    E. Grandjean, Universal Quantifiers and Time Complexity of Random Access Machines, Math. Syst. Theory (1985), 171–187.Google Scholar
  6. [6]
    E. Grandjean, First-Order Spectra with One Variable, in: E. Börger (Ed.), “Computation Theory and Logic”, Lecture Notes in Computer Science Nr. 270, Springer 1987, 166–180.Google Scholar
  7. [7]
    Y. Gurevich, Toward logic tailord for computational complexity, in: M. M. Richter et al. (Eds), Computation and Proof Theory, Springer Lecture Notes in Mathematics Nr. 1104 (1984), 175–216.Google Scholar
  8. [8]
    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
  9. [9]
    N. Immerman, Relational Queries Computable in Polynomial Time, Inf. and Control 68 (1986), 86–104.Google Scholar
  10. [10]
    N. Immerman, Languages that Capture Complexity Classes, SIAM J. Comput. 16 (1987), 760–778.CrossRefGoogle Scholar
  11. [11]
    N. Immerman, Expressibility and Parallel Complexity, Tech. Report 546, Yale University, Department of Computer Science (1987).Google Scholar
  12. [12]
    N. Immerman, Expressibility as a Complexity Measure: Results and Directions, Proc. of 2nd Conf. on Structure in Complexity Theory (1987), 194–202.Google Scholar
  13. [13]
    N. Immerman, Nondeterministic space is closed under complementation, SIAM J. Comput. 17 (1988), 935–939.CrossRefGoogle Scholar
  14. [14]
    N. Immerman, Descriptive and Computational Complexity, in: J. Hartmanis (Ed.), Computational Complexity Theory, Proc. of AMS Symposia in Appl. Math. 38 (1989), 75–91.Google Scholar
  15. [15]
    N. Jones and W. Laaser, Complete problems for deterministic polynomial time, Theoret. Comp. Sci 3 (1977), 105–117.Google Scholar
  16. [16]
    R. Karp and R. Lipton, Turing Machines that Take Advice, in: Logic and Algorithmic, Monographie Nr. 30 de L'Enseignement Mathématique, Genève 1982, 255–273.Google Scholar
  17. [17]
    K. Ko, On self-reducibility and weak P-selectivity, J. of Comput. Syst. Sci. 26 (1983), 209–221.Google Scholar
  18. [18]
    K. Ko and U. Schöning, On circuit-size complexity and the low hierarchy in NP, SIAM J. Comput. 14 (1985), 41–51.CrossRefGoogle Scholar
  19. [19]
    C. Papadimitriou and M. Yannakakis, The complexity of facets (and some facets of complexity), Proceedings of 14th STOC 1982, 255–260.Google Scholar
  20. [20]
    R. Szelepcsényi, The Method of Forced Enumeration for Nondeterministic Automata, Acta Informatica 26, (1988), 279–284.Google Scholar
  21. [21]
    U. Schöning, A Low and a High Hierarchy within NP, J. Comput. Syst. Sci. 27 (1983), 14–28.Google Scholar
  22. [22]
    U. Schöning, Complexity and Structure, Springer Lecture Notes in Computer Science Nr. 211 (1986).Google Scholar
  23. [23]
    M. Vardi, Complexity of Relational Query Languages, Proc. of 14th STOC (1982), 137–146.Google Scholar
  24. [24]
    K. Wagner, Bounded Query Computations, Proceedings of 3rd Conference on Structure in Complexity Theory 1988, 260–277.Google Scholar
  25. [25]
    G. Wechsung (and K. Wagner), On the Boolean cloure of NP, Proceedings of FCT 85, Lecture Notes in Computer Science Nr. 199, Springer 1985, 485–493.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Erich Grädel
    • 1
  1. 1.Mathematisches InstitutUniversität BaselBasel

Personalised recommendations