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On the intrinsic complexity of learning recursive functions
 In Proceedings of the Twelfth Annual Conference on Computational Learning Theory
, 1999
"... The intrinsic complexity of learning compares the difficulty of learning classes of objects by using some reducibility notion. For several types of learning recursive functions, both natural complete classes are exhibited and necessary and sufficient conditions for completeness are derived. Informal ..."
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Cited by 5 (1 self)
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The intrinsic complexity of learning compares the difficulty of learning classes of objects by using some reducibility notion. For several types of learning recursive functions, both natural complete classes are exhibited and necessary and sufficient conditions for completeness are derived. Informally, a class is complete iff both its topological structure is highly complex while its algorithmic structure is easy. Some selfdescribing classes turn out to be complete. Furthermore, the structure of the intrinsic complexity is shown to be much richer than the structure of the mind change complexity, though in general, intrinsic complexity and mind change complexity can behave “orthogonally”. 1.
On OneSided Versus TwoSided Classification
 Forschungsberichte Mathematische Logik 25 / 1996, Mathematisches Institut, Universit at
, 1996
"... Onesided classifiers are computable devices which read the characteristic function of a set and output a sequence of guesses which converges to 1 iff the set on the input belongs to the given class. Such a classifier is twosided if the sequence of its output in addition converges to 0 on sets not ..."
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Cited by 4 (3 self)
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Onesided classifiers are computable devices which read the characteristic function of a set and output a sequence of guesses which converges to 1 iff the set on the input belongs to the given class. Such a classifier is twosided if the sequence of its output in addition converges to 0 on sets not belonging to the class. The present work obtains the below mentioned results for onesided classes (= \Sigma 0 2 classes) w.r.t. four areas: Turing complexity, 1reductions, index sets and measure. There are onesided classes which are not twosided. This can have two reasons: (1) the class has only high Turing complexity. Then there are some oracles which allow to construct noncomputable twosided classifiers. (2) The class is difficult because of some topological constraints and then there are also no nonrecursive twosided classifiers. For case (1), several results are obtained to localize the Turing complexity of certain types of onesided sets. The concepts of 1reduction, 1completene...