In computational complexity theory, most conjectures that two complexity classes are equal (or not equal, as the case may be) can be relativized to an oracle. Sometimes, as in the case of P = NP, one can obtain contradictory relativizations; i.e., there exists an oracle A such that P^A = NP^A and an oracle B such that P^B ≠ NP^B.

In the case of contradictory relativizations, it is tempting to hypothesize that if, for example, P^B ≠ NP^B for "most" oracles B, then P ≠ NP in the "real" (unrelativized) world. This heuristic was seriously proposed by Bennett and Gill as the "random oracle hypothesis," for a specific precise definition of "most oracles." However, the random oracle hypothesis was disproved by Kurtz. Later, another conjecture was proposed along similar lines: the "generic oracle hypothesis," with a different precise definition of "most oracles." But the generic oracle hypothesis was also disproved, by Foster.