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Inductive Inference Machines (IlMs) attempt to identify functions given only input-output pairs of the functions. Probabilistic IlMs are defined, as is the probability that a probabilistic IlM identifies a function with respect to two common identification criteria: EX and BC. Let ID denote either of these criteria. Then ID/sub prob/(p) is the family of sets of functions U for which there is a probabilistic IlM identifying every f /spl epsi/ U with probability /spl ges/ p. It is shown that for all positive integers n, ID/sub prob/(1/n) is properly contained in ID/sub prob/(1/(n+1)), and that this discrete hierarchy is the "finest" possible. This hierarchy is related to others in the literature.
Leonard Pitt (Thu,) studied this question.