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).
References
SHOWING 1-4 OF 4 REFERENCES
A New Approach to the Sensitivity Conjecture
- Mathematics, Computer ScienceITCS
- 2015
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.
Complexity measures and decision tree complexity: a survey
- Computer ScienceTheor. Comput. Sci.
- 2002
On the degree of boolean functions as real polynomials
- Computer Science, MathematicsSTOC '92
- 1992
A tight lower bound is found of Ω(logn) on the degree needed to represent any Boolean function that depends onn variables on the level of real polynomial.
Variations on the Sensitivity Conjecture
- MathematicsTheory Comput.
- 2011
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.