Recursively enumerable sets and degrees
Recursively enumerable sets and degrees
Prudence and other conditions on formal language learning
Information and Computation
On the intrinsic complexity of learning
Information and Computation
The intrinsic complexity of language identification
Journal of Computer and System Sciences
Machine Inductive Inference and Language Identification
Proceedings of the 9th Colloquium on Automata, Languages and Programming
Proceedings of the Symposium "Rekursive Kombinatorik" on Logic and Machines: Decision Problems and Complexity
Mitosis in computational complexity
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
Autoreducibility, mitoticity, and immunity
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
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For the natural notion of splitting classes into two disjoint subclasses via a recursive classifier working on texts, the question is addressed how these splittings can look in the case of learnable classes. Here the strength of the classes is compared using the strong and weak reducibility from intrinsic complexity. It is shown that, for explanatorily learnable classes, the complete classes are also mitotic with respect to weak and strong reducibility, respectively. But there is a weak complete class which cannot be split into two classes which are of the same complexity with respect to strong reducibility. It is shown that for complete classes for behaviourally correct learning, one half of each splitting is complete for this learning notion as well. Furthermore, it is shown that explanatorily learnable and recursively enumerable classes always have a splitting into two incomparable classes; this gives an inductive inference counterpart of Sacks Splitting Theorem from recursion theory.