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Author Long, Timothy J. ♦ Selman, Alan L.
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©1986
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Abstract Baker, Gill, and Solovay constructed sparse sets $\textit{A}$ and $\textit{B}$ such that $P(\textit{A})$ ≠ $NP(\textit{A})$ and $NP(\textit{B})$ ≠ $co-NP(\textit{B}).$ In contrast to their results, we prove that P = NP if and only if for every tally language $\textit{T},$ $P(\textit{T})$ = NP( $\textit{T}),$ and that NP = co-NP if and only if for every tally language $\textit{T},$ $NP(\textit{T})$ = $co-NP(\textit{T}).$ We show that the polynomial hierarchy collapses if and only if there is a sparse set $\textit{S}$ such that the polynomial hierarchy relative to $\textit{S}$ collapses. Similar results are obtained for several other complexity classes.
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 1986-05-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 33
Issue Number 3
Page Count 10
Starting Page 618
Ending Page 627

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Source: ACM Digital Library