About: En route to the log-rank conjecture: new reductions and equivalent formulations

Facets (new session)
Description
Metadata
Settings
- owl:sameAs
- Inference Rule:

About: En route to the log-rank conjecture: new reductions and equivalent formulations Goto Sponge NotDistinct Permalink

An Entity of Type : http://linked.opendata.cz/ontology/domain/vavai/Vysledek, within Data Space : linked.opendata.cz associated with source document(s)

Attributes	Values
rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	We prove that several measures in communication complexity are equivalent, up to polynomial factors in the logarithm of the rank of the associated matrix: deterministic communication complexity, randomized communication complexity, information cost and zero-communication cost. This shows that in order to prove the log-rank conjecture, it suffices to show that low-rank matrices have efficient protocols in any of the aforementioned measures. Furthermore, we show that the notion of zero-communication complexity is equivalent to an extension of the common discrepancy bound. Linial et al. [Combinatorica, 2007] showed that the discrepancy of a sign matrix is lower-bounded by an inverse polynomial in the logarithm of the associated matrix. We show that if these results can be generalized to the extended discrepancy, this will imply the log-rank conjecture. We prove that several measures in communication complexity are equivalent, up to polynomial factors in the logarithm of the rank of the associated matrix: deterministic communication complexity, randomized communication complexity, information cost and zero-communication cost. This shows that in order to prove the log-rank conjecture, it suffices to show that low-rank matrices have efficient protocols in any of the aforementioned measures. Furthermore, we show that the notion of zero-communication complexity is equivalent to an extension of the common discrepancy bound. Linial et al. [Combinatorica, 2007] showed that the discrepancy of a sign matrix is lower-bounded by an inverse polynomial in the logarithm of the associated matrix. We show that if these results can be generalized to the extended discrepancy, this will imply the log-rank conjecture. (en)
Title	En route to the log-rank conjecture: new reductions and equivalent formulations En route to the log-rank conjecture: new reductions and equivalent formulations (en)
skos:prefLabel	En route to the log-rank conjecture: new reductions and equivalent formulations En route to the log-rank conjecture: new reductions and equivalent formulations (en)
skos:notation	RIV/67985840:_____/14:00434135!RIV15-GA0-67985840
http://linked.open...avai/riv/aktivita	I P
http://linked.open...avai/riv/aktivity	I, P(GBP202/12/G061)
http://linked.open...vai/riv/dodaniDat	2015
http://linked.open...aciTvurceVysledku	Gavinsky, Dmitry
http://linked.open.../riv/druhVysledku	D - Článek ve sborníku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Matematický ústav AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	14489
http://linked.open...ai/riv/idVysledku	RIV/67985840:_____/14:00434135
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	automata theory; matrix algebra; associated matrices; communication complexity (en)
http://linked.open.../riv/klicoveSlovo	associated matrices automata theory communication complexity matrix algebra
http://linked.open...ontrolniKodProRIV	[322A00E2C3F8]
http://linked.open...v/mistoKonaniAkce	Copenhagen
http://linked.open...i/riv/mistoVydani	Berlin
http://linked.open...i/riv/nazevZdroje	Automata, Languages, and Programming
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Center of excellence - Institute for theoretical computer science (CE-ITI)
http://linked.open...UplatneniVysledku	2014
http://linked.open...iv/tvurceVysledku	Gavinsky, Dmitry Lovett, S.
http://linked.open...vavai/riv/typAkce	WRD - Světová
http://linked.open.../riv/zahajeniAkce	2014-07-08 (xsd:date)
number of pages	11 (xsd:int)
http://bibframe.org/vocab/doi	10.1007/978-3-662-43948-7_43
http://purl.org/ne...btex#hasPublisher	Springer-Verlag
https://schema.org/isbn	978-3-662-43947-0

Faceted Search & Find service v1.16.118 as of Jun 21 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 07.20.3240 as of Jun 21 2024, on Linux (x86_64-pc-linux-gnu), Single-Server Edition (126 GB total memory, 58 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software