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URN: urn:nbn:de:0030-drops-64593
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On the Limits of Gate Elimination

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Abstract

Although a simple counting argument shows the existence of Boolean functions of exponential circuit complexity, proving superlinear circuit lower bounds for explicit functions seems to be out of reach of the current techniques. There has been a (very slow) progress in proving linear lower bounds with the latest record of 3 1/86*n-o(n). All known lower bounds are based on the so-called gate elimination technique. A typical gate elimination argument shows that it is possible to eliminate several gates from an optimal circuit by making one or several substitutions to the input variables and repeats this inductively. In this note we prove that this method cannot achieve linear bounds of cn beyond a certain constant c, where c depends only on the number of substitutions made at a single step of the induction.

BibTeX - Entry

@InProceedings{golovnev_et_al:LIPIcs:2016:6459,
  author =	{Alexander Golovnev and Edward A. Hirsch and Alexander Knop and Alexander S. Kulikov},
  title =	{{On the Limits of Gate Elimination}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{46:1--46:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-016-3},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{58},
  editor =	{Piotr Faliszewski and Anca Muscholl and Rolf Niedermeier},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6459},
  URN =		{urn:nbn:de:0030-drops-64593},
  doi =		{10.4230/LIPIcs.MFCS.2016.46},
  annote =	{Keywords: circuit complexity, lower bounds, gate elimination}
}

Keywords: circuit complexity, lower bounds, gate elimination
Seminar: 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)
Issue date: 2016
Date of publication: 2016


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