Let A(x) be the characteristic function of A. Consider the function Fk (x1, . . . , xk) = A(x1) · · ·A(xk). We show that if F A k can be computed with fewer than k queries to some set X then A ∈ P/poly. A generalization of this result has applications to bounded query classes, circuits, and enumerability. In particular we obtain the following. (1) Assuming… (More)