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Title: Mitotic classes in inductive inference
Authors: Jain, S. 
Stephan, F. 
Keywords: Inductive inference
Mitotic classes
Recursion theory
Issue Date: 2008
Citation: Jain, S., Stephan, F. (2008). Mitotic classes in inductive inference. SIAM Journal on Computing 38 (4) : 1283-1299. ScholarBank@NUS Repository.
Abstract: For the natural notion of splitting classes into two disjoint subclasses via a recursive classifier working on texts, the question of how these splittings can look in the case of learnable classes is addressed. 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 weakly complete class that 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 behaviorally 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 the Sacks splitting theorem from recursion theory. © 2008 Society for Industrial and Applied Mathematics.
Source Title: SIAM Journal on Computing
ISSN: 00975397
DOI: 10.1137/070700577
Appears in Collections:Staff Publications

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