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, bounded width, and bounded 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. For EX- learning (as well as for BC-learning, where a final sequence of cor...

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