Theory of Computing Systems

, Volume 33, Issue 2, pp 151–170

Resource-Bounded Measure and Learnability

Authors

  • W. Lindner
    • Abteilung Theoretische Informatik, Universität Ulm, 89081 Ulm, Germany lindner$@informatik.uni-ulm.de, schuler$@informatik.uni-ulm.de
  • R. Schuler
    • Abteilung Theoretische Informatik, Universität Ulm, 89081 Ulm, Germany lindner$@informatik.uni-ulm.de, schuler$@informatik.uni-ulm.de
  • O. Watanabe
    • Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo 152-8552, Japan watanabe@is.titech.ac.jp

DOI: 10.1007/s002249910010

Cite this article as:
Lindner, W., Schuler, R. & Watanabe, O. Theory Comput. Systems (2000) 33: 151. doi:10.1007/s002249910010

Abstract.

We consider the resource-bounded measure of polynomial-time learnable subclasses of polynomial-size circuits. We show that if EXP ≠ MA, then every PAC-learnable subclass of P/poly has EXP-measure zero. We introduce a nonuniformly computable variant of resource-bounded measure and show that, for every fixed polynomial q , any polynomial-time learnable subclass of circuits of size q has measure zero with respect to P/poly. We relate our results to the question of whether the class of Boolean circuits is polynomial-time learnable.

Copyright information

© 2000 Springer-Verlag New York Inc.