NDLI: Mitotic Classes in Inductive Inference

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Jain, Sanjay Stephan, Frank
Copyright Year	2008
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.
Starting Page	1283
Ending Page	1299
Page Count	17
File Format	PDF
ISSN	00975397
DOI	10.1137/070700577
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	4
Volume Number	38
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2008-07-23
Access Restriction	Subscribed
Subject Keyword	reducibilities Recursively (computably) enumerable sets and degrees recursion theory Other degrees and reducibilities mitotic classes Computational learning theory inductive inference
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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