Query order and NP-completeness

Abstract

The effect of query order on NP-completeness is investigated. A sequence D/spl I.oarr/=(D/sub 1/,...,D/sub k/) of decision problems is defined to be sequentially complete for NP if each D/sub i//spl isin/NP and every problem in NP can be decided in polynomial time with one query to each of D/sub 1/,...,D/sub 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/spl ges/2, there is a sequence D/spl I.oarr/=(d/sub 1/,...,D/sub k/) such that D is sequentially complete for NP, but no nontrivial permutation (D(i/sub 1/),...,D(i/sub k/)) of D/spl I.oarr/ is sequentially complete for NP. It follows that such a sequence D/spl I.oarr/ exists if there is any strongly positive, p-computable probability measure /spl nu/ such that "/sub p/(NP)/spl ne/0.