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Abstract: This paper discusses advances, due to the work of Cai, Naik, and Sivakumar [CNS95] and Glaßer [Gla00], in the complexity class collapses that follow if NP has sparse hard sets under reductions weaker than (full) truth-table reductions. (Update)
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BibTeX entry: (Update)
@misc{ er-moment,
author = "Christian Glaßer and Lane A. Hemaspaandra",
title = "A Moment of Perfect Clarity II: Consequences of Sparse Sets Hard for NP
with Respect to Weak Reductions",
url = "citeseer.ist.psu.edu/516974.html" }
Citations (may not include all citations):163 NP is as easy as detecting unique solutions (context) - Valiant, Vazirani - 1986
122 A comparison of polynomial time reducibilities (context) - Ladner, Lynch et al. - 1975
70 Sparse complete sets for NP: Solution of a conjecture of Ber.. (context) - Mahaney - 1982
49 On polynomial-time bounded truth-table reducibility of NP se.. - Ogiwara, Watanabe - 1991
40 and sparse Turing-complete sets for NP (context) - Kadin, NP - 1989
33 Reductions to sets of low information content - Arvind, Han et al. - 1993
33 How hard are sparse sets (context) - Hemachandra, Ogiwara et al. - 1992
23 How reductions to sparse sets collapse the polynomial-time h.. - Young - 1992
20 the existence of hard sparse sets under weak reductions - Cai, Naik et al. - 1995
15 Six hypotheses in search of a theorem - Buhrman, Fortnow et al. - 1997
15 New collapse consequences of NP having small circuits (context) - obler, Watanabe - 1999
14 Upper bounds for the complexity of sparse and tally descript.. - Arvind, obler et al. - 1996
8 Sparse sets and reducibilities (context) - Mahaney - 1986
8 Sparse sets versus complexity classes - Cai, Ogihara - 1997
5 Personal Communication (context) - Sivakumar - 2000
[Article contains additional citations not shown here]
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