The polynomial-time hierarchy and sparse oraclesThe polynomial-time hierarchy and sparse oracles

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 Author Balczar, Jose L. ♦ Book, Ronald V. ♦ Schning, Uwe 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 Questions about the polynomial-time hierarchy are studied. In particular, the questions, “Does the polynomial-time hierarchy collapse?” and “Is the union of the hierarchy equal to PSPACE?” are considered, along with others comparing the union of the hierarchy with certain probabilistic classes. In each case it is shown that the answer is “yes” if and only if for every sparse set $\textit{S},$ the answer is “yes” when the classes are relativized to $\textit{S}$ if and only if there exists a sparse set $\textit{S}$ such that the answer is “yes” when the classes are relativized to $\textit{S}.$ Thus, in each case the question is answered if it is answered for any arbitrary sparse oracle set.Long and Selman first proved that the polynomial-time hierarchy collapses if and only if for every sparse set $\textit{S},$ the hierarchy relative to $\textit{S}$ collapses. This result is re-proved here by a different technique. 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 15 Starting Page 603 Ending Page 617

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Source: ACM Digital Library