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.CCC.2020.26
URN: urn:nbn:de:0030-drops-125786
URL: https://drops.dagstuhl.de/opus/volltexte/2020/12578/
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Saks, Michael ; Santhanam, Rahul

Circuit Lower Bounds from NP-Hardness of MCSP Under Turing Reductions

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LIPIcs-CCC-2020-26.pdf (0.4 MB)


Abstract

The fundamental Minimum Circuit Size Problem is a well-known example of a problem that is neither known to be in 𝖯 nor known to be NP-hard. Kabanets and Cai [Kabanets and Cai, 2000] showed that if MCSP is NP-hard under "natural" m-reductions, superpolynomial circuit lower bounds for exponential time would follow. This has triggered a long line of work on understanding the power of reductions to MCSP. Nothing was known so far about consequences of NP-hardness of MCSP under general Turing reductions. In this work, we consider two structured kinds of Turing reductions: parametric honest reductions and natural reductions. The latter generalize the natural reductions of Kabanets and Cai to the case of Turing-reductions. We show that NP-hardness of MCSP under these kinds of Turing-reductions imply superpolynomial circuit lower bounds for exponential time.

BibTeX - Entry

@InProceedings{saks_et_al:LIPIcs:2020:12578,
  author =	{Michael Saks and Rahul Santhanam},
  title =	{{Circuit Lower Bounds from NP-Hardness of MCSP Under Turing Reductions}},
  booktitle =	{35th Computational Complexity Conference (CCC 2020)},
  pages =	{26:1--26:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-156-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{169},
  editor =	{Shubhangi Saraf},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12578},
  URN =		{urn:nbn:de:0030-drops-125786},
  doi =		{10.4230/LIPIcs.CCC.2020.26},
  annote =	{Keywords: Minimum Circuit Size Problem, Turing reductions, circuit lower bounds}
}

Keywords: Minimum Circuit Size Problem, Turing reductions, circuit lower bounds
Collection: 35th Computational Complexity Conference (CCC 2020)
Issue Date: 2020
Date of publication: 17.07.2020


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