Please use this identifier to cite or link to this item: https://doi.org/10.1016/j.jcss.2006.09.001
Title: On the learnability of vector spaces
Authors: Harizanov, V.S.
Stephan, F. 
Keywords: 0-thin and 1-thin spaces
Computational learning theory
Inductive inference
Learning algebraic structures
Recursively enumerable vector spaces
Issue Date: Feb-2007
Source: Harizanov, V.S., Stephan, F. (2007-02). On the learnability of vector spaces. Journal of Computer and System Sciences 73 (1) : 109-122. ScholarBank@NUS Repository. https://doi.org/10.1016/j.jcss.2006.09.001
Abstract: The central topic of the paper is the learnability of the recursively enumerable subspaces of V∞ / V, where V∞ is the standard recursive vector space over the rationals with (countably) infinite dimension and V is a given recursively enumerable subspace of V∞. It is shown that certain types of vector spaces can be characterized in terms of learnability properties: V∞ / V is behaviourally correct learnable from text iff V is finite-dimensional, V∞ / V is behaviourally correct learnable from switching the type of information iff V is finite-dimensional, 0-thin or 1-thin. On the other hand, learnability from an informant does not correspond to similar algebraic properties of a given space. There are 0-thin spaces W1 and W2 such that W1 is not explanatorily learnable from an informant, and the infinite product (W1)∞ is not behaviourally correct learnable from an informant, while both W2 and the infinite product (W2)∞ are explanatorily learnable from an informant. © 2006 Elsevier Inc. All rights reserved.
Source Title: Journal of Computer and System Sciences
URI: http://scholarbank.nus.edu.sg/handle/10635/103811
ISSN: 00220000
DOI: 10.1016/j.jcss.2006.09.001
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