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引用次数: 4

摘要

研究了查询顺序对np完备性的影响。A序列D/spl I.oarr/=(D/sub 1/,…如果每个D/下标i//spl都是/NP,并且NP中的每个问题都可以在多项式时间内通过对D/下标1/,…的查询来决定,则定义决策问题的D/下标k/)对于NP是顺序完备的。D/下标k/按这个顺序。结果表明,如果NP包含Ambos-Spies, Fleischhack, and Huwig(1987)意义上的p-泛型语言,则对于每一个整数k/spl ges/2,存在一个序列D/spl I.oarr/=(D/ sub 1/,…),D/下标k/)使得D对于NP是顺序完全的,但不存在非平凡排列(D(i/下标1/),…,D /spl i .oarr/的D(i/sub k/))对于NP是顺序完全的。因此,如果存在任何强正的、p可计算的概率测度/spl nu/使得“/sub p/(NP)/spl ne/0”,则存在这样的序列D/spl I.oarr/。
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Query order and NP-completeness
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.
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