On the Learnability of the Uncomputable

Within Valiant'smodel of learning as formalized by Kearns, we show that computable total predicates for two formallyuncomputable problems the classical Halting Problem, and the Halting Problem relative to a speci ed oracle are formallylearnable fromexamples, to arbitrarily high accuracy with arbitrarily high con dence, under any probability distribution. The Halting Problem relative to the oracle is learnable in time polynomial in the measures of accuracy, con dence, and the length of the learned predicate. The classical Halting Problem is learnable in expected time polynomialin the measures of accuracy, con dence, and the 1 , =16th percentile length and run-time of programs which do halt on their inputs these quantities are always nite. Equivalently, the mean length and run-time maybe substituted for the percentile values in the time complexity statement. The proofs are constructive. While the problems are learnable, they are not polynomially learnable, even though we do derive ...

• Type: Conference
• Year: 1996
• Where: ICML
• Authors: Richard H. Lathrop
• Keywords: Classical Halting Problem, ICML 1996, Machine Learning, Percentile Length, Polynomial Time Bounds