Theoretical Computer Science
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The effect of query order on NP-completeness is investigated. A sequence D = (D1,...,Dk) of decision problems is defined to be sequentially complete for NP if each Di is in NP and every problem in NP can be decided in polynomial time with one query to each of D1,...,Dk 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 = (D1,...,Dk) such that D is sequentially complete for NP, but no nontrivial permutation 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 relative to which NP does not have p-measure 0.