Query order and NP-completeness

The effect of query order on NP-completeness is investigated. A sequence D&oarr;=(D₁,…,D_k) of decision problems is defined to be sequentially complete for NP if each D_i ∈NP and every problem in NP can be decided in polynomial time with one query to each of D₁,…,D_k in this order. It is shown that, if NP contains a language that is p-generic in the sense of Ambos-Spies, Fleischhack, and Huwig (1987), then for every integer k⩾2, there is a sequence D&oarr;=(d₁,…,D _k) such that D is sequentially complete for NP, but no nontrivial permutation (D(i₁),…,D(i_k)) of D&oarr; is sequentially complete for NP. It follows that such a sequence D&oarr; exists if there is any strongly positive, p-computable probability measure ν such that ”_p(NP)≠0