There exists an oracle, relative to which P ≠ NP and each ofthe following properties hold: (i) allΣp2-complete sets are p-isomorphic; (ii)P-inseparable pairs of sets in NP do not exist; (iii) intractablepublic-key cryptosystems do not exist; and (iv) NP-complete sets areclosed under union of disjoint sets. Remarkably, these properties allfollow from one oracle construction, namely, it is proved that there isan oracle A such that every two disjoint sets in NPAare P-separable, and ΣP2=∪{DTIME(2p)| p is a polynomial}. Additional related relativizationresults are presented
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机译：存在一个相对于P≠NP且每个相对于
以下属性成立：（i）全部
Σ p 2 -完全集是p同构的; （ii）
NP中的P分不开的对不存在; （iii）棘手的
公钥密码系统不存在; （iv）NP完全集是
在不交集的并集下关闭。值得注意的是，所有这些属性
遵循一个甲骨文的构造，即证明有
oracle A ，使得NP A 中的每两个不交集
是P可分离的，并且Σ P 2 =∪{DTIME（2 p
）| p 是一个多项式}。相关的相对化
结果呈现
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