Abstract
We consider representation classes of polynomial query complexity in Angluin's exact learning model with all three possible combinations of membership and (proper) equivalence queries allowed. We show that in all three cases, polynomial query complexity implies already polynomial-time learnability where the learner additionally has access to an oracle in Σ p2 . As an application, it follows that boolean circuits are polynomial-time learnable with equivalence queries and the help of an oracle in Σ p2 . Our results are based on known combinatorial properties characterizing polynomial query complexity and a careful application of hashing-techniques.
The work of the second author has partially been done while visiting Departamento L.S.I., Univ. Politecnica de Catalunya.
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© 1997 Springer-Verlag Berlin Heidelberg
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Köbler, J., Lindner, W. (1997). Oracles in Σ p2 are sufficient for exact learning. In: Li, M., Maruoka, A. (eds) Algorithmic Learning Theory. ALT 1997. Lecture Notes in Computer Science, vol 1316. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63577-7_49
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DOI: https://doi.org/10.1007/3-540-63577-7_49
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