On the Structure of Polynomial Time Reducibility
Journal of the ACM (JACM)
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Some structural properties of polynomial reducibilities and sets in NP
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Theoretical Computer Science - Australasian computer science
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The existence of minimal degrees is investigated for several polynomial reducibilities. It is shown that no set has minimal degree with respect to polynomial many-one or Turing reducibility. This extends a result of Ladner in which only recursive sets are considered. A polynomial reducibility ≤hT is defined. This reducibility is a strengthening of polynomial Turing reducibility, and its properties relate to the P = ? NP question. For this new reducibility, a set of minimal degree is constructed under the assumption that P = NP. However, the set constructed is nonrecursive, and it is shown that no recursive set is of minimal ≤ hT degree.