A Communication Game Related to the Sensitivity Conjecture

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10368746" target="_blank" >RIV/00216208:11320/17:10368746 - isvavai.cz</a>

Result on the web

<a href="http://www.theoryofcomputing.org/articles/v013a007/" target="_blank" >http://www.theoryofcomputing.org/articles/v013a007/</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4086/toc.2017.v013a007" target="_blank" >10.4086/toc.2017.v013a007</a>

Result language

angličtina

Original language name

A Communication Game Related to the Sensitivity Conjecture

Original language description

One of the major outstanding foundational problems about Boolean functions is the sensitivity conjecture, which asserts that the degree of a Boolean function is bounded above by some fixed power of its sensitivity. We propose an attack on the sensitivity conjecture in terms of a novel two-player communication game. A lower bound of the form n^Omega(1) on the cost of this game would imply the sensitivity conjecture. To investigate the problem of bounding the cost of the game, three natural (stronger) variants of the question are considered. For two of these variants, protocols are presented that show that the hoped-for lower bound does not hold. These protocols satisfy a certain monotonicity property, and we show that the cost of any monotone protocol satisfies a strong lower bound in the original variant. There is an easy upper bound of sqrt(n) on the cost of the game. We also improve slightly on this upper bound. This game and its connection to the sensitivity conjecture was independently discovered by Andy Drucker (arXiv:1706.07890).

Czech name

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Czech description

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Type

J_ost - Miscellaneous article in a specialist periodical

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

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Continuities

R - Projekt Ramcoveho programu EK

Publication year

2017

Confidentiality

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

Name of the periodical

Theory of Computing [online]

ISSN

1557-2862

e-ISSN

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Volume of the periodical

2017

Issue of the periodical within the volume

13

Country of publishing house

US - UNITED STATES

Number of pages

18

Pages from-to

1-18

UT code for WoS article

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EID of the result in the Scopus database

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