Identifying nearly minimal Gödel numbers from additional information

  • Rūsiņš Freivalds
  • Ognian Botuscharov
  • Rolf Wiehagen
Selected Papers Analogical and Inductive Inference

DOI: 10.1007/3-540-58520-6_56

Part of the Lecture Notes in Computer Science book series (LNCS, volume 872)
Cite this paper as:
Freivalds R., Botuscharov O., Wiehagen R. (1994) Identifying nearly minimal Gödel numbers from additional information. In: Arikawa S., Jantke K.P. (eds) Algorithmic Learning Theory. Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence), vol 872. Springer, Berlin, Heidelberg

Abstract

A new identification type close to the identification of minimal Gödel numbers is considered. The type is defined by allowing as input both the graph of the target function and an arbitrary upper bound of the minimal index of the target function in a Gödel numbering of all partial recursive functions. However, the result of the inference has to be bounded by a fixed function from the given bound. Results characterizing the dependence of this identification type from the underlying Gödel numbering are obtained. In particular, it is shown that for a wide class of Gödel numberings, the class of all recursive functions can be identified even for “small” bounding functions.

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Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Rūsiņš Freivalds
    • 1
  • Ognian Botuscharov
    • 2
  • Rolf Wiehagen
    • 3
  1. 1.Institute of Mathematics and Computer ScienceUniversity of LatviaRigaLatvia
  2. 2.Department of Computer ScienceUniversity of SofiaSofiaBulgaria
  3. 3.Department of Computer ScienceUniversity of KaiserslauternKaiserslauternGermany

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