1,608 research outputs found
PAC Learning, VC Dimension, and the Arithmetic Hierarchy
We compute that the index set of PAC-learnable concept classes is
-complete within the set of indices for all concept classes of
a reasonable form. All concept classes considered are computable enumerations
of computable classes, in a sense made precise here. This family of
concept classes is sufficient to cover all standard examples, and also has the
property that PAC learnability is equivalent to finite VC dimension
Refinment of the "up to a constant" ordering using contructive co-immunity and alike. Application to the Min/Max hierarchy of Kolmogorov complexities
We introduce orderings between total functions f,g: N -> N which refine the
pointwise "up to a constant" ordering <=cte and also insure that f(x) is often
much less thang(x). With such orderings, we prove a strong hierarchy theorem
for Kolmogorov complexities obtained with jump oracles and/or Max or Min of
partial recursive functions. We introduce a notion of second order conditional
Kolmogorov complexity which yields a uniform bound for the "up to a constant"
comparisons involved in the hierarchy theorem.Comment: 41 page
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