Adaptive versus nonadaptive queries to NP and p-selective sets

We prove that P = NP follows if for some , the class of functions that are computable in polynomial time by nonadaptively accessing an oracle in NP is effectively included in PF^NP[k⌈log n⌉— 1], the class of functions that are computable in polynomial k⌈log n⌉— 1 queries to an oracle in NP.?We draw several observations and relationships between the following two properties of a complexity class : whether there exists a truthtable hard p-selective language for , and whether polynomially-many nonadaptive queries to can be answered by making O(log n)-many adaptive queries to (in symbols, whether ). Among these, we show that if there exists an NP-hard p-selective set under truth-table reductions, then . However, if , then these two properties are equivalent. Received: November 1, 1996.