• Corpus ID: 30493317

A Note on a Communication Game

@article{Drucker2017ANO,
  title={A Note on a Communication Game},
  author={Andrew Drucker},
  journal={ArXiv},
  year={2017},
  volume={abs/1706.07890}
}
  • 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… 
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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.

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