Inductive Inference with Additional Information

摘要

We consider the problem of inductively inferring a grammar for a language, given (positive) examples of the language and putative (possibly faulty) grammars for the complement of the language. The criterion of success is identification in the limit, defined by E. M. Gold (1967, Inform. and Control10, 447–474). Additional information is useful insofar as it allows the identification of language classes that would not be identified with positive examples alone. An infinite sequence of grammars past some finite position are correct for the complement of the input language, is not as useful a form of additional information as a single correct grammar for the complement. Grammars that are almost correct for the complement (that is, that make finitely many errors) are not as useful as correct grammars, and the usefulness of a grammar decreases with increasing numbers of errors.