On the Amount of Nonconstructivity in Learning Recursive Functions

  • Rūsiņš Freivalds
  • Thomas Zeugmann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6648)

Abstract

Nonconstructive proofs are a powerful mechanism in mathematics. Furthermore, nonconstructive computations by various types of machines and automata have been considered by e.g., Karp and Lipton [] and Freivalds []. They allow to regard more complicated algorithms from the viewpoint of much more primitive computational devices. The amount of nonconstructivity is a quantitative characterization of the distance between types of computational devices with respect to solving a specific problem.

In the present paper, the amount of nonconstructivity in learning of recursive functions is studied. Different learning types are compared with respect to the amount of nonconstructivity needed to learn the whole class of general recursive functions. Upper and lower bounds for the amount of nonconstructivity needed are proved.

Keywords

inductive inference recursive functions nonconstructivity 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Rūsiņš Freivalds
    • 1
  • Thomas Zeugmann
    • 2
  1. 1.Institute of Mathematics and Computer Science, University of Latvia, Raiņa Bulvāris 29, Riga, LV-1459Latvia
  2. 2.Division of Computer ScienceHokkaido UniversitySapporoJapan

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