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We consider how much error a fixed depth Boolean circuit must make in computing the parity function. We show that with an exponential bound of the form exp(n") on the size of the circuits, they make a 50% error on all possible inputs, asymptotically and uniformly. As a consequence, we show that a random oracle set A separates PSPACE from the entire polynomial-time hierarchy with probability one. 0 1989 Academic PRESS, IUC.doi:10.1016/0022-0000(89)90033-0 fatcat:mkqhwf2x2vfp3cmpdqprjn3abm