Lower Bounds for Elimination via Weak Regularity

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10368568" target="_blank" >RIV/00216208:11320/17:10368568 - isvavai.cz</a>

Result on the web

<a href="http://drops.dagstuhl.de/opus/volltexte/2017/7012/pdf/LIPIcs-STACS-2017-21.pdf" target="_blank" >http://drops.dagstuhl.de/opus/volltexte/2017/7012/pdf/LIPIcs-STACS-2017-21.pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.STACS.2017.21" target="_blank" >10.4230/LIPIcs.STACS.2017.21</a>

Result language

angličtina

Original language name

Lower Bounds for Elimination via Weak Regularity

Original language description

We consider the problem of elimination in communication complexity, that was first raised by Ambainis et al. and later studied by Beimel et al. [4] for its connection to the famous direct sum question. In this problem, let f be any boolean function. Alice and Bob get k inputs x_1, . . . , x_k and y_1, . . . , y_k respectively. They want to output a k-bit vector v, such that there exists one index i for which v_i is not equal to f(x_i, y_i). We prove a general result lower bounding the randomized communication complexity of the elimination problem for f using its discrepancy. Consequently, we obtain strong lower bounds for the functions InnerProduct and Greater-Than, that work for exponentially larger values of k than the best previous bounds. To prove our result, we use a pseudo-random notion called regularity that was first used by Raz and Wigderson. We show that functions with small discrepancy are regular. We also observe that a weaker notion, that we call weak-regularity, already implies hardness of elimination. Finally, we give a different proof, borrowing ideas from Viola, to show that Greater-Than is weakly regular.

Czech name

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Czech description

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Type

D - Article in proceedings

CEP classification

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OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

—

Continuities

R - Projekt Ramcoveho programu EK

Publication year

2017

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection

34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)

ISBN

978-3-95977-028-6

ISSN

1868-8969

e-ISSN

neuvedeno

Number of pages

14

Pages from-to

1-14

Publisher name

Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik

Place of publication

Dagstuhl, Germany

Event location

Hannover

Event date

Mar 8, 2017

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

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