An improved protocol for the exactly-N problem

Nati Linial*, Adi Shraibman*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations


In the 3-players exactly-N problem the players need to decide whether x + y + z = N for inputs x, y, z and fixed N. This is the first problem considered in the multiplayer Number On the Forehead (NOF) model. Even though this is such a basic problem, no progress has been made on it throughout the years. Only recently have explicit protocols been found for the first time, yet no improvement in complexity has been achieved to date. The present paper offers the first improved protocol for the exactly-N problem. This improved protocol has also interesting consequences in additive combinatorics. As we explain below, it yields a higher lower bound on the possible density of corner-free sets in [N] × [N].

Original languageAmerican English
Title of host publication36th Computational Complexity Conference, CCC 2021
EditorsValentine Kabanets
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Number of pages8
ISBN (Electronic)9783959771931
StatePublished - 1 Jul 2021
Event36th Computational Complexity Conference, CCC 2021 - Virtual, Toronto, Canada
Duration: 20 Jul 202123 Jul 2021

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Conference36th Computational Complexity Conference, CCC 2021
CityVirtual, Toronto

Bibliographical note

Publisher Copyright:
© Nati Linial and Adi Shraibman; licensed under Creative Commons License CC-BY 4.0


  • Communication complexity
  • Corner-free sets
  • Number-on-the-forehead

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