Can complexity theory benefit from Learning Theory?

  • Tibor Hegedüs
Position Papers Learnability
Part of the Lecture Notes in Computer Science book series (LNCS, volume 667)


We show that the results achieved within the framework of Computational Learning Theory are relevant enough to have non-trivial applications in other areas of Computer Science, namely in Complexity Theory. Using known results on efficient query-learnability of some Boolean concept classes, we prove several (co-NP-completeness) results on the complexity of certain decision problems concerning representability of general Boolean functions in special forms.


  1. [1]
    D. Angluin, ”Learning k-term DNF Formulas Using Queries and Counterexamples”, Technical Report, Yale University, YALE/DCS/RR-559, 1987.Google Scholar
  2. [2]
    D. Angluin, ”Computational Learning Theory: Survey and Selected Bibliography”, in: Proceedings of the 24th Annual ACM Symposium on the Theory of Computing, 1992, pp. 351–369.Google Scholar
  3. [3]
    M. Anthony and N. Biggs, Computational Learning Theory, Cambridge University Press, Cambridge, 1992.Google Scholar
  4. [4]
    M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman, San Francisco, 1979.Google Scholar
  5. [5]
    T. Hegedüs, “Computational Limitations on PAC and On-Line Learning over the Boolean Domain: a Comparison”, submitted for publication.Google Scholar
  6. [6]
    T. Hegedüs and N. Megiddo, ”On the Geometric Separability of Boolean Functions”, submitted for publication.Google Scholar
  7. [7]
    W. Maass and Gy. Turán, “On the Complexity of Learning from Counterexamples”, in: Proceedings of the 30th Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Angeles, 1989, pp. 262–267.Google Scholar
  8. [8]
    W. Maass and Gy. Turán, “Algorithms and Lower Bounds for On-Line Learning of Geometrical Concepts”, Report 316, IIG-Report Series, Graz University of Technology, 1991.Google Scholar
  9. [9]
    W. Maass and Gy. Turán, “How Fast can a Threshold Gate Learn?” Report 321, IIG-Report Series, Graz University of Technology, 1991.Google Scholar
  10. [10]
    L. Pitt and L. Valiant, ”Computational Limitations on Learning from Examples”, Journal of the ACM 35 (1988) 965–984.Google Scholar
  11. [11]
    L. Valiant, ”A Theory of the Learnable”, Communications of the ACM 27 (1984) 1134–1142.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Tibor Hegedüs
    • 1
  1. 1.Department of Computer ScienceComenius UniversityBratislavaSlovakia

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