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DOI: 10.4230/LIPIcs.FSTTCS.2015.236
URN: urn:nbn:de:0030-drops-56613
URL: http://drops.dagstuhl.de/opus/volltexte/2015/5661/
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Hitchcock, John M. ; Pavan, A.

On the NP-Completeness of the Minimum Circuit Size Problem

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Abstract

We study the Minimum Circuit Size Problem (MCSP): given the truth-table of a Boolean function f and a number k, does there exist a Boolean circuit of size at most k computing f? This is a fundamental NP problem that is not known to be NP-complete. Previous work has studied consequences of the NP-completeness of MCSP. We extend this work and consider whether MCSP may be complete for NP under more powerful reductions. We also show that NP-completeness of MCSP allows for amplification of circuit complexity. We show the following results. - If MCSP is NP-complete via many-one reductions, the following circuit complexity amplification result holds: If NP cap co-NP requires 2^n^{Omega(1)-size circuits, then E^NP requires 2^Omega(n)-size circuits. - If MCSP is NP-complete under truth-table reductions, then EXP neq NP cap SIZE(2^n^epsilon) for some epsilon> 0 and EXP neq ZPP. This result extends to polylog Turing reductions.

BibTeX - Entry

@InProceedings{hitchcock_et_al:LIPIcs:2015:5661,
  author =	{John M. Hitchcock and A. Pavan},
  title =	{{On the NP-Completeness of the Minimum Circuit Size Problem}},
  booktitle =	{35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)},
  pages =	{236--245},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-97-2},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{45},
  editor =	{Prahladh Harsha and G. Ramalingam},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/5661},
  URN =		{urn:nbn:de:0030-drops-56613},
  doi =		{10.4230/LIPIcs.FSTTCS.2015.236},
  annote =	{Keywords: Minimum Circuit Size, NP-completeness, truth-table reductions, circuit complexity}
}

Keywords: Minimum Circuit Size, NP-completeness, truth-table reductions, circuit complexity
Seminar: 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)
Issue Date: 2015
Date of publication: 11.12.2015


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