Query Order and NP - Completeness 1

The eeect of query order on NP-completeness is investigated. A sequence ~ D = (D 1 ; : : : ; D k) of decision problems is deened to be sequentially complete for NP if each D i 2 NP and every problem in NP can be decided in polynomial time with one query to each of D 1 ; : : : ; 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 3], then for every integer k 2, there is a sequence ~ D = (D 1 ; : : : ; D k) such that ~ D is sequentially complete for NP, but no nontrivial permutation (D i1 ; : : : ; D i k) of ~ D is sequentially complete for NP. It follows that such a sequence ~ D exists if there is any strongly positive, p-computable probability measure such that p (NP) 6 = 0.