Can complexity theory benefit from Learning Theory?
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.
- D. Angluin, ”Learning k-term DNF Formulas Using Queries and Counterexamples”, Technical Report, Yale University, YALE/DCS/RR-559, 1987.Google Scholar
- 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
- M. Anthony and N. Biggs, Computational Learning Theory, Cambridge University Press, Cambridge, 1992.Google Scholar
- M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman, San Francisco, 1979.Google Scholar
- T. Hegedüs, “Computational Limitations on PAC and On-Line Learning over the Boolean Domain: a Comparison”, submitted for publication.Google Scholar
- T. Hegedüs and N. Megiddo, ”On the Geometric Separability of Boolean Functions”, submitted for publication.Google Scholar
- 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
- 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
- W. Maass and Gy. Turán, “How Fast can a Threshold Gate Learn?” Report 321, IIG-Report Series, Graz University of Technology, 1991.Google Scholar
- L. Pitt and L. Valiant, ”Computational Limitations on Learning from Examples”, Journal of the ACM 35 (1988) 965–984.Google Scholar
- L. Valiant, ”A Theory of the Learnable”, Communications of the ACM 27 (1984) 1134–1142.Google Scholar