A Communication Game Related to the Sensitivity Conjecture

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

A Communication Game Related to the Sensitivity Conjecture

Popis výsledku v původním jazyce

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).

Název v anglickém jazyce

A Communication Game Related to the Sensitivity Conjecture

Popis výsledku anglicky

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).

Druh

J_ost - Ostatní články v recenzovaných periodicích

CEP obor

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OECD FORD obor

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

Projekt

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Návaznosti

R - Projekt Ramcoveho programu EK

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

Theory of Computing [online]

ISSN

1557-2862

e-ISSN

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Svazek periodika

2017

Číslo periodika v rámci svazku

13

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

18

Strana od-do

1-18

Kód UT WoS článku

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EID výsledku v databázi Scopus

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