Abstract
Investigated is algorithmic learning, in the limit, of correct programs for recursive functions f from both input/output examples of f and several interesting varieties of approximate additional (algorithmic) information about f. Specifically considered, as such approximate additional information about f, are Rose's frequency computations for f and several natural generalizations from the literature, each generalization involving programs for restricted trees of recursive functions which have f as a branch. Considered as the types of trees are those with bounded variation, finite width, and finite rank.
For the case of learning final correct programs for recursive functions, EX-learning, where the additional information involves frequency computations, an insightful and interestingly complex combinatorial characterization of learning power is presented as a function of the frequency parameters. Pitt has previously characterized the learning power of probabilistic machines in terms of the size of equally powerful teams of (deterministic) machines. For EX-learning (as well as for BC-learning, where a final sequence of correct programs is learned), for the cases of providing the types of additional information considered in this paper, the optimal machine team size is determined such that the entire class of recursive functions is learnable.
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Case, J., Kaufmann, S., Kinber, E., Kummer, M. (1995). Learning recursive functions from approximations. In: Vitányi, P. (eds) Computational Learning Theory. EuroCOLT 1995. Lecture Notes in Computer Science, vol 904. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59119-2_174
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DOI: https://doi.org/10.1007/3-540-59119-2_174
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