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License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2016.42
URN: urn:nbn:de:0030-drops-57437
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/5743/
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Hitchcock, John M. ; Shafei, Hadi

Autoreducibility of NP-Complete Sets

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Abstract

We study the polynomial-time autoreducibility of NP-complete sets and obtain separations under strong hypotheses for NP. Assuming there is a p-generic set in NP, we show the following:

- For every k >= 2, there is a k-T-complete set for NP that is k-T autoreducible, but is not k-tt autoreducible or (k-1)-T autoreducible.

- For every k >= 3, there is a k-tt-complete set for NP that is k-tt autoreducible, but is not (k-1)-tt autoreducible or (k-2)-T autoreducible.

- There is a tt-complete set for NP that is tt-autoreducible, but is not btt-autoreducible.

Under the stronger assumption that there is a p-generic set in NP cap coNP, we show:

- For every k >= 2, there is a k-tt-complete set for NP that is k-tt autoreducible, but is not (k-1)-T autoreducible.

Our proofs are based on constructions from separating NP-completeness notions. For example, the construction of a 2-T-complete set for NP that is not 2-tt-complete also separates 2-T-autoreducibility from 2-tt-autoreducibility.

BibTeX - Entry

@InProceedings{hitchcock_et_al:LIPIcs:2016:5743,
  author =	{John M. Hitchcock and Hadi Shafei},
  title =	{{Autoreducibility of NP-Complete Sets}},
  booktitle =	{33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)},
  pages =	{42:1--42:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-001-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{47},
  editor =	{Nicolas Ollinger and Heribert Vollmer},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/5743},
  URN =		{urn:nbn:de:0030-drops-57437},
  doi =		{10.4230/LIPIcs.STACS.2016.42},
  annote =	{Keywords: computational complexity, NP-completeness, autoreducibility, genericity}
}

Keywords: computational complexity, NP-completeness, autoreducibility, genericity
Collection: 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)
Issue Date: 2016
Date of publication: 16.02.2016

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