A new approach to the sensitivity conjecture

Justin Gilmer, Michal Koucký, Michael Saks

Research output: Chapter in Book/Report/Conference proceedingConference contribution

14 Scopus citations

Abstract

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 contrast to the situation for the two variants) we show that the cost of any monotone protocol satisfies a strong lower bound.

Original languageEnglish (US)
Title of host publicationITCS 2015 - Proceedings of the 6th Innovations in Theoretical Computer Science
PublisherAssociation for Computing Machinery, Inc
Pages247-254
Number of pages8
ISBN (Electronic)9781450333337
DOIs
StatePublished - Jan 11 2015
Event6th Conference on Innovations in Theoretical Computer Science, ITCS 2015 - Rehovot, Israel
Duration: Jan 11 2015Jan 13 2015

Publication series

NameITCS 2015 - Proceedings of the 6th Innovations in Theoretical Computer Science

Other

Other6th Conference on Innovations in Theoretical Computer Science, ITCS 2015
Country/TerritoryIsrael
CityRehovot
Period1/11/151/13/15

All Science Journal Classification (ASJC) codes

  • Computational Theory and Mathematics

Keywords

  • Communication complexity
  • Decision trees
  • Degree of Boolean functions
  • Sensitivity
  • Sensitivity conjecture

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