• Corpus ID: 30493317

A Note on a Communication Game

  title={A Note on a Communication Game},
  author={Andrew Drucker},
  • Andrew Drucker
  • Published 24 June 2017
  • Mathematics, Computer Science
  • ArXiv
We describe a communication game, and a conjecture about this game, whose proof would imply the well-known Sensitivity Conjecture asserting a polynomial relation between sensitivity and block sensitivity for Boolean functions. The author defined this game and observed the connection in Dec. 2013 - Jan. 2014. The game and connection were independently discovered by Gilmer, Kouck\'y, and Saks, who also established further results about the game (not proved by us) and published their results in… 
2 Citations

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This work improves Nisan Szegedy's result to a cost of $O(n^{4696})$ by providing a technique to identify whether a set of codewords can be used as a viable strategy in this game.

Induced subgraphs of hypercubes and a proof of the Sensitivity Conjecture

It is proved that the sensitivity and degree of a boolean function are polynomially related, solving an outstanding foundational problem in theoretical computer science, the Sensitivity Conjecture of Nisan and Szegedy.



A New Approach to the Sensitivity Conjecture

This work proposes an attack on the sensitivity conjecture in terms of a novel two-player communication game, and shows that the cost of any monotone protocol satisfies a strong lower bound.

An O(n0.4732) upper bound on the complexity of the GKS communication game

  • M. Szegedy
  • Computer Science
    Electron. Colloquium Comput. Complex.
  • 2015
An $5\cdot n^{\log_{30}5}$ upper bund is given on the complexity of the communication game introduced by G. Gilmer, M. Kouck\'y and M. Saks to study the Sensitivity Conjecture, improving on their $\sqrt{999\over 1000}$ bound.

Weak Parity

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  • N. Nisan
  • Computer Science, Mathematics
    STOC '89
  • 1989
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The Equivalence of Two Problems on the Cube

On induced subgraphs of the cube

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We present a selection of known as well as new variants of the Sensitivity Conjecture and point out some weaker versions that are also open.