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Author Homer, Steven
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©1987
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Abstract 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 $≤\textit{h}\textit{T}$ 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 ≤ $\textit{h}\textit{T}$ degree.
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 1987-04-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 34
Issue Number 2
Page Count 12
Starting Page 480
Ending Page 491


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Source: ACM Digital Library