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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITCS.2020.58
URN: urn:nbn:de:0030-drops-117431
URL: https://drops.dagstuhl.de/opus/volltexte/2020/11743/
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Gál, Anna ; Robere, Robert

Lower Bounds for (Non-Monotone) Comparator Circuits

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LIPIcs-ITCS-2020-58.pdf (0.5 MB)


Abstract

Comparator circuits are a natural circuit model for studying the concept of bounded fan-out computations, which intuitively corresponds to whether or not a computational model can make "copies" of intermediate computational steps. Comparator circuits are believed to be weaker than general Boolean circuits, but they can simulate Branching Programs and Boolean formulas. In this paper we prove the first superlinear lower bounds in the general (non-monotone) version of this model for an explicitly defined function. More precisely, we prove that the n-bit Element Distinctness function requires Ω((n/ log n)^(3/2)) size comparator circuits.

BibTeX - Entry

@InProceedings{gl_et_al:LIPIcs:2020:11743,
  author =	{Anna G{\'a}l and Robert Robere},
  title =	{{Lower Bounds for (Non-Monotone) Comparator Circuits}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{58:1--58:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Thomas Vidick},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/11743},
  URN =		{urn:nbn:de:0030-drops-117431},
  doi =		{10.4230/LIPIcs.ITCS.2020.58},
  annote =	{Keywords: comparator circuits, circuit complexity, Nechiporuk, lower bounds}
}

Keywords: comparator circuits, circuit complexity, Nechiporuk, lower bounds
Seminar: 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)
Issue Date: 2020
Date of publication: 10.01.2020


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