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.ITCS.2020.58
URN: urn:nbn:de:0030-drops-117431
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/11743/
Go to the corresponding LIPIcs Volume Portal

Gál, Anna ; Robere, Robert

Lower Bounds for (Non-Monotone) Comparator Circuits

pdf-format:
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
Collection: 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)
Issue Date: 2020
Date of publication: 06.01.2020

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI