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DOI: 10.4230/LIPIcs.FSTTCS.2014.445
URN: urn:nbn:de:0030-drops-48621
URL: http://drops.dagstuhl.de/opus/volltexte/2014/4862/
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Mandal, Debasis ; Pavan, A. ; Venugopalan, Rajeswari

Separating Cook Completeness from Karp-Levin Completeness Under a Worst-Case Hardness Hypothesis

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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.

BibTeX - Entry

@InProceedings{mandal_et_al:LIPIcs:2014:4862,
  author =	{Debasis Mandal and A. Pavan and Rajeswari Venugopalan},
  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 =	{Venkatesh Raman and S. P. Suresh},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2014/4862},
  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}
}

Keywords: Cook reduction, Karp reduction, NP-completeness, Turing completeness, many-one completeness
Seminar: 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)
Issue Date: 2014
Date of publication: 11.12.2014


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