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DOI: 10.4230/LIPIcs.FSTTCS.2014.445
Separating Cook Completeness from Karp-Levin Completeness Under a Worst-Case Hardness Hypothesis

Authors: Debasis Mandal, A. Pavan, and Rajeswari Venugopalan

Published in: LIPIcs, Volume 29, 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)

Abstract
We show that there is a language that is Turing complete for NP but not many-one complete for NP, under a worst-case hardness hypothesis. Our hypothesis asserts the existence of a non-deterministic, double-exponential time machine that runs in time O(2^2^n^c) (for some c > 1) accepting Sigma^* whose accepting computations cannot be computed by bounded-error, probabilistic machines running in time O(2^2^{beta * 2^n^c) (for some beta > 0). This is the first result that separates completeness notions for NP under a worst-case hardness hypothesis.
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Debasis Mandal, A. Pavan, and Rajeswari Venugopalan. Separating Cook Completeness from Karp-Levin Completeness Under a Worst-Case Hardness Hypothesis. In 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 29, pp. 445-456, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{mandal_et_al:LIPIcs.FSTTCS.2014.445,
  author =	{Mandal, Debasis and Pavan, A. and Venugopalan, Rajeswari},
  title =	{{Separating Cook Completeness from Karp-Levin Completeness Under a Worst-Case Hardness Hypothesis}},
  booktitle =	{34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)},
  pages =	{445--456},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-77-4},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{29},
  editor =	{Raman, Venkatesh and Suresh, S. P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2014.445},
  URN =		{urn:nbn:de:0030-drops-48621},
  doi =		{10.4230/LIPIcs.FSTTCS.2014.445},
  annote =	{Keywords: Cook reduction, Karp reduction, NP-completeness, Turing completeness, many-one completeness}
}
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