On distribution-specific learning with membership queries versus pseudorandom generation

Abstract

We consider a weak version of pseudorandom function generators and show that their existence is equivalent to the non-learnability of Boolean circuits in Valiant’s pac-learning model with membership queries on the uniform distribution. Furthermore, we show that this equivalence holds still for the case of non-adaptive membership queries and for any (non-trivial) p-samplable distribution. © Springer-Verlag Berlin Heidelberg 2000.