Resource-Bounded Measure and Learnability

Abstract.

We consider the resource-bounded measure of polynomial-time learnable subclasses of polynomial-size circuits. We show that if EXP ≠ MA, then every PAC-learnable subclass of P/poly has EXP-measure zero. We introduce a nonuniformly computable variant of resource-bounded measure and show that, for every fixed polynomial q , any polynomial-time learnable subclass of circuits of size q has measure zero with respect to P/poly. We relate our results to the question of whether the class of Boolean circuits is polynomial-time learnable.