Abstract
Abstract Identification by algorithmic devices of programs for computable functions from their graphs is a well studied problem in learning theory. Freivalds and Chen consider identification of “minimal” and “nearly minimal” programs for functions from their graphs. The present paper solves the following question left open by Chen: Is it the case that for any collection of computable functions, C , such that some machine can finitely learn a nearly minimal (n + 1)-error program for every function in C , there exists another machine that can learn in the limit an n-error program (which need not be nearly minimal) for every function in C ? We answer this question negatively.
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