R. Freivalds et al., IDENTIFYING NEARLY MINIMAL GODEL NUMBERS FROM ADDITIONAL INFORMATION, Annals of mathematics and artificial intelligence, 23(1-2), 1998, pp. 199-209
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 m
inimal index of the target function in a Godel numbering of all partia
l recursive functions. However, the result of the inference has to be
bounded by a fixed function from the given bound. Results characterizi
ng the dependence of this identification type from the underlying numb
ering are obtained. In particular, it is shown that for a wide class o
f Godel numberings, the class of all recursive functions can be identi
fied even for small bounding functions.