Classical results of Bennett and Gill (1981) show that with probability 1, $P^A \neq NP^A$ relative to a random oracle $A$, and with probability 1, $P^\pi \neq NP^\pi \cap coNP^\pi$ relative to a random permutation $Pi$. Whether $P^A = NP^A \cap coNP^A$ holds relative to a random oracle $A$ remains ... more >>>