Characterizing Language Identification in Terms of Computable Numberings

Identification of programs for computable functions from their graphs and identification of grammars (r. e. indices) for recursively enumerable languages from positive data are two extensively studied problems in the recursion theoretic framework of inductive inference. In the context of function identification, Freivalds, Kinber, and Wiehagen have shown that only those collections of functions, S, are identifiable in the limit for which there exists