Identifying nearly minimal Gödel numbers from additional information

Authors:
Rūsiņš Freivalds;Ognian Botuscharov;Rolf Wiehagen
Affiliations:
Institute of Mathematics and Computer Science, University of Latvia, Raina bulv. 29, LV‐1459 Riga, Latvia E-mail: rusins@cclu.lv;Department of Computer Science, University of Sofia, Sofia, Bulgaria;Department of Computer Science, University of Kaiserslautern, P.O. Box 3049, D‐67653 Kaiserslautern, Germany E-mail: wiehagen@informatik.uni‐kl.de
Venue:
Annals of Mathematics and Artificial Intelligence
Year:
1998

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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 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.