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- W2078408075 abstract "Whether or not P is properly included in NP is currently one of the most important open problems in computer science. A deterministic polynomially time-bounded reducibility ⩽ r P and its nondeterministic analogue ⩽ r NP provide a positive relativization of this problem if P = NP is equivalent to P · r(B) = NP · r(B) for all oracle sets B . Initial attempts to relativize the P = ?NP problem considered reducibilities which are not known to yield positive relativizations. Baker, Gill, and Solovay [1] provided oracle sets B and B ′ such that P · T( B ) ≠ NP · T( B ) and P · T( B′ ) = NP · T(B'); however, it remains open whether P ⩞ NP or, equivalently, whether the polynomially time-bounded Turing reducibility of Cook ( in “Proceedings, 3rd Annual ACM Symposium on Theory of Computing, 1971,” pp. 151–158) provides a positive relativization of the problem. Book, Long, and Selman ( SIAM J. Comput. 13 (1984), 461–487) found a restricted form of Cook's reducibility that does provide a positive relativization. Several reducibilities between polynomially time-bounded Turing reducibility and polynomially time-bounded many-one reducibility are investigated for their ability to positively relativize the P = ?NP problem." @default.
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- W2078408075 title "Positive relativizations of the P = ? NP problem" @default.
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