In 1987, Blum and Impagliazzo, using techniques of Hartmanis and Hemachandra and Rackoff, showed that ifP=NPthenP(G)=NP(G)∩coNP(G)=UP(G), whereGis a generic oracle. They leave open the question as to whether these collapses occur at higher levels of the polynomial-time hierarchy, i.e.,Δ p k (G)=Σ p k (G)∩Π p k (G)=UΔ p k (G) fork⩾2. Here we give a negative answer to these questions. In fact, we demonstrate that, relative to any generic oracleGand for everyk⩾2, there exists a tally set inUΔ p k (G)∩Π p k (G) but not inΔ p k (G) by showing an exponential lower bound of a certain type of families of constant-depth circuits. An immediate corollary is that generic oracles separateΣ p k ∩Π p k andΔ p k . We also show that related results hold for type-2 complexity.