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

@article{Szegedy2015AnOU, title={An O(n0.4732) upper bound on the complexity of the GKS communication game}, author={Mario Szegedy}, journal={Electron. Colloquium Comput. Complex.}, year={2015}, volume={TR15} }

We give an $5\cdot n^{\log_{30}5}$ upper bund on the complexity of the communication game introduced by G. Gilmer, M. Kouck\'y and M. Saks \cite{saks} to study the Sensitivity Conjecture \cite{linial}, improving on their $\sqrt{999\over 1000}\sqrt{n}$ bound. We also determine the exact complexity of the game up to $n\le 9$.

## 7 Citations

### An improvement of the upper bound for GKS communication game

- Computer ScienceArXiv
- 2020

A slight improvement of Ingram's method is proposed and a protocol with cost of $O(n^{0.4693})$ is designed for the GKS game.

### A Note on a Communication Game

- Mathematics, Computer ScienceArXiv
- 2017

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…

### A Tighter Relation between Sensitivity and Certificate Complexity

- Computer ScienceArXiv
- 2016

A better upper bound of the sensitivity conjecture is given, based on a deep investigation on the structure of theensitivity graph, and a tighter relationship between $C_0(f)$ and $s-0( f)$ for functions with $s_1(f)=2$.

### On the Sensitivity Conjecture

- Mathematics, Computer ScienceICALP
- 2016

The sensitivity conjecture is shown to be far from being understood, as there is an exponential gap between the known upper and lower bounds relating bs(f) and s(f).

### A Tighter Relation Between Sensitivity Complexity and Certificate Complexity

- Computer Science, MathematicsCOCOON
- 2017

A better upper bound is given for certificate complexity and block sensitivity, and a tighter relationship is provided between the 0-certificate complexity and 0-s sensitivity for functions with small 1-sensitivity.

### Low-Sensitivity Functions from Unambiguous Certificates

- Computer ScienceITCS
- 2016

A quadratic separation between the tree-sensitivity and decision tree complexity of Boolean functions is provided, disproving a conjecture of Gopalan, Servedio, Tal, and Wigderson (CCC 2016).

### On the Sensitivity Complexity of k-Uniform Hypergraph Properties

- Mathematics, Computer ScienceSTACS
- 2017

This result disproves a conjecture of Babai, which conjectures that the sensitivity complexity of k-uniform hypergraph properties is at least Ω (nk/2), and shows that for many classes of transitive Boolean functions the minimum achievable sensitivity complexity can be O(N1/3).

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