A New Approach to the Sensitivity Conjecture

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10316311" target="_blank" >RIV/00216208:11320/15:10316311 - isvavai.cz</a>

Výsledek na webu

<a href="http://doi.acm.org/10.1145/2688073.2688096" target="_blank" >http://doi.acm.org/10.1145/2688073.2688096</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1145/2688073.2688096" target="_blank" >10.1145/2688073.2688096</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A New Approach to the Sensitivity Conjecture

Popis výsledku v původním jazyce

One of the major outstanding foundational problems about boolean functions is the sensitivity conjecture, which (in one of its many forms) asserts that the degree of a boolean function (i.e. the minimum degree of a real polynomial that interpolates the function) is bounded above by some fixed power of its sensitivity (which is the maximum vertex degree of the graph defined on the inputs where two inputs are adjacent if they differ in exactly one coordinate and their function values are different). We propose an attack on the sensitivity conjecture in terms of a novel two-player communication game. A strong enough lower bound 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 (in con

Název v anglickém jazyce

A New Approach to the Sensitivity Conjecture

Popis výsledku anglicky

One of the major outstanding foundational problems about boolean functions is the sensitivity conjecture, which (in one of its many forms) asserts that the degree of a boolean function (i.e. the minimum degree of a real polynomial that interpolates the function) is bounded above by some fixed power of its sensitivity (which is the maximum vertex degree of the graph defined on the inputs where two inputs are adjacent if they differ in exactly one coordinate and their function values are different). We propose an attack on the sensitivity conjecture in terms of a novel two-player communication game. A strong enough lower bound 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 (in con

Druh

D - Stať ve sborníku

CEP obor

IN - Informatika

OECD FORD obor

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Projekt

<a href="/cs/project/GA14-10003S" target="_blank" >GA14-10003S: Omezené typy výpočtů: algoritmy, modely, složitost</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2015

Kód důvěrnosti údajů

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

Název statě ve sborníku

Proceedings of the 2015 Conference on Innovations in Theoretical Computer Science, {ITCS} 2015

ISBN

978-1-4503-3333-7

ISSN

—

e-ISSN

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Počet stran výsledku

8

Strana od-do

247-254

Název nakladatele

ACM

Místo vydání

NEW YORK

Místo konání akce

Rehovot, Israel

Datum konání akce

11. 1. 2015

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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