On the intrinsic complexity of learning recursive functions

  • Authors:
  • Sanjay Jain;Efim Kinber;Christophe Papazian;Carl Smith;Rolf Wiehagen

  • Affiliations:
  • School of Computing, National University of Singapore, 119260 Singapore;Computer Science Department, Sacred Heart University, Fairfield, CT;Département de Mathématique et d'Informatique, Ecole Normale Supérieure de Lyon, F-69364 Lyon Cedex 07, France;Department of Computer Science, University of Maryland, College Park, MD;Fachbereich Informatik, Universität Kaiserslautern, D-67653 Kaiserslautern, Germany

  • Venue:
  • Information and Computation
  • Year:
  • 2003

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Abstract

The intrinsic complexity of learning compares the difficulty of learning classes of objects by using some reducibility notion. For several types of learning recursive functions, both natural complete classes are exhibited and necessary and sufficient conditions for completeness are derived. Informally, a class is complete iff both its topological structure is highly complex while its algorithmic structure is easy. Some self-describing classes turn out to be complete. Furthermore, the structure of the intrinsic complexity is shown to be much richer than the structure of the mind change complexity, though in general, intrinsic complexity and mind change complexity can behave "orthogonally".