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.APPROX-RANDOM.2018.48
URN: urn:nbn:de:0030-drops-94525
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9452/
Go to the corresponding LIPIcs Volume Portal

Koroth, Sajin ; Meir, Or

Improved Composition Theorems for Functions and Relations

pdf-format:
LIPIcs-APPROX-RANDOM-2018-48.pdf (0.5 MB)

Abstract

One of the central problems in complexity theory is to prove super-logarithmic depth bounds for circuits computing a problem in P, i.e., to prove that P is not contained in NC^1. As an approach for this question, Karchmer, Raz and Wigderson [Mauricio Karchmer et al., 1995] proposed a conjecture called the KRW conjecture, which if true, would imply that P is not cotained in NC^{1}.
Since proving this conjecture is currently considered an extremely difficult problem, previous works by Edmonds, Impagliazzo, Rudich and Sgall [Edmonds et al., 2001], Håstad and Wigderson [Johan Håstad and Avi Wigderson, 1990] and Gavinsky, Meir, Weinstein and Wigderson [Dmitry Gavinsky et al., 2014] considered weaker variants of the conjecture. In this work we significantly improve the parameters in these variants, achieving almost tight lower bounds.

BibTeX - Entry

@InProceedings{koroth_et_al:LIPIcs:2018:9452,
  author =	{Sajin Koroth and Or Meir},
  title =	{{Improved Composition Theorems for Functions and Relations}},
  booktitle =	{Approximation, Randomization, and Combinatorial  Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)},
  pages =	{48:1--48:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-085-9},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{116},
  editor =	{Eric Blais and Klaus Jansen and Jos{\'e} D. P. Rolim and David Steurer},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9452},
  URN =		{urn:nbn:de:0030-drops-94525},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2018.48},
  annote =	{Keywords: circuit complexity, communication complexity, KRW conjecture, composition}
}

Keywords: circuit complexity, communication complexity, KRW conjecture, composition
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)
Issue Date: 2018
Date of publication: 13.08.2018

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