Identifying nearly minimal Gödel numbers from additional information

Abstract

A new identification type close to the identification of minimal Godel 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 Godel 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 Godel numberings, the class of all recursive functions can be identified even for small bounding functions.