25th Annual Symposium onFoundations of Computer Science, 1984. (1984)
Singer Island, FL
Oct. 24, 1984 to Oct. 26, 1984
L. Pitt , Yale University
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.
L. Pitt, "A Characterization Of Probabilistic Inference," 25th Annual Symposium onFoundations of Computer Science, 1984.(FOCS), Singer Island, FL, 1984, pp. 485-494.