Algorithmic Learning Theory pp 91-99
Identifying nearly minimal Gödel numbers from additional information
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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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