Synthesizing Noise-Tolerant Language Learners

An index for an r.e. class of languages (by definition) generates a sequence of grammars defining the class. An index for an indexed family of languages (by definition) generates a sequence of decision procedures defining the family. F. Stephan’s model of noisy data is employed, in which, roughly, correct data crops up infinitely often, and incorrect data only finitely often. Studied, then, is the synthesis from indices for r.e. classes and for indexed families of languages of various kinds of noise-tolerant language-learners for the corresponding classes or families indexed. Many positive results, as well as some negative results, are presented regarding the existence of such synthesizers. The proofs of most of the positive results yield, as pleasant corollaries, strict subset-principle or tell-tale style characterizations for the noise-tolerant learnability of the corresponding classes or families indexed.