The existence of string functions, which are not polynomial time computable, but whose graph is checkable in polynomial time, is a basic assumption in cryptography. We prove that in the framework of algebraic complexity, there are no such families of polynomial functions of -bounded degree over fields of characteristic zero. The proof relies on a polynomial upper bound on the approximative comp...

We consider representation classes of polynomial query complexity in Angluin's exact learning model with all three possible combinations of membership and (proper) equivalence queries allowed. We show that in all three cases, polynomial query complexity implies already polynomial-time learnability where the learner additionally has access to an oracle in p 2. As an application, it follows that ...