# 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} }

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

### An Upper Bound on the GKS Game via Max Bipartite Matching

- MathematicsArXiv
- 2017

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

- MathematicsAnnals of Mathematics
- 2019

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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