关于NP集到稀疏集的约简

[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference Pub Date : 1991-06-30 DOI:10.1109/SCT.1991.160246

S. Homer, L. Longpré

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引用次数: 55

摘要

M. Ogiwara和O. Watanabe(1990)证明了如果SAT是可约为稀疏集的有界真值表，则P=NP。在本工作中，作者简化了他们的证明，加强了结果，并利用它得到了几个新的结果。这些新结果包括:主要定理在NP集的对数真值表和对数图灵约简中的应用;主要定理的推广，其结果与多项式层次的任意层次上的主要结果相似;以及P不=NP的oracle的构造，但存在NP完备集，f(n)-tt-可约为一个计数集，对于(log n)中的任意f(n)

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On reductions of NP sets to sparse sets

M. Ogiwara and O. Watanabe (1990) showed that if SAT is bounded truth-table reducible to a sparse set, then P=NP. In the present work, the authors simplify their proof, strengthen the result, and use it to obtain several new results. Among the new results are the following: applications of the main theorem to log-truth-table and log-Turing reductions of NP sets to sparse sets; generalizations of the main theorem which yield results similar to the main result at arbitrary levels of the polynomial hierarchy; and the construction of an oracle relative to which P not=NP but there are NP-complete sets which are f(n)-tt-reducible to a tally set, for any f(n) in Omega (log n).<>

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[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference

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