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 finitely dimensional, V ∞/V is behaviourally correct learnable from switching 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 W 1 and W 2 such that W 1 is not explanatorily learnable from informant and the infinite product (W 1)∞ is not behaviourally correct learnable, while W 2 and the infinite product (W 2)∞ are both explanatorily learnable from informant.
Valentina Harizanov was partially supported by the UFF grant of the George Washington University.
Frank Stephan was supported by the Deutsche Forschungsgemeinschaft (DFG) Heisenberg grant Ste 967/1-1.
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Harizanov, V.S., Stephan, F. (2002). On the Learnability of Vector Spaces. In: Cesa-Bianchi, N., Numao, M., Reischuk, R. (eds) Algorithmic Learning Theory. ALT 2002. Lecture Notes in Computer Science(), vol 2533. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36169-3_20
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