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A New Approach to the Sensitivity Conjecture

The result's identifiers

  • Result code in 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>

  • Result on the web

    <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>

Alternative languages

  • Result language

    angličtina

  • Original language name

    A New Approach to the Sensitivity Conjecture

  • Original language description

    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

  • Czech name

  • Czech description

Classification

  • Type

    D - Article in proceedings

  • CEP classification

    IN - Informatics

  • OECD FORD branch

Result continuities

  • Project

    <a href="/en/project/GA14-10003S" target="_blank" >GA14-10003S: Restricted computations: Algorithms, models, complexity</a><br>

  • Continuities

    I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2015

  • Confidentiality

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

Data specific for result type

  • Article name in the collection

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

  • ISBN

    978-1-4503-3333-7

  • ISSN

  • e-ISSN

  • Number of pages

    8

  • Pages from-to

    247-254

  • Publisher name

    ACM

  • Place of publication

    NEW YORK

  • Event location

    Rehovot, Israel

  • Event date

    Jan 11, 2015

  • Type of event by nationality

    WRD - Celosvětová akce

  • UT code for WoS article