An Upper Bound on the GKS Game via Max Bipartite Matching

DeVon Ingram

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arXiv · 1712.01149

An Upper Bound on the GKS Game via Max Bipartite Matching

DeVon Ingram

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Abstract

The sensitivity conjecture is a longstanding conjecture concerning the relationship between the degree and sensitivity of a Boolean function. In 2015, a communication game was formulated by Justin Gilmer, Michal Kouck\'{y}, and Michael Saks to attempt to make progress on this conjecture. Andrew Drucker independently formulated this game. Shortly after the creation of the GKS game, Nisan Szegedy obtained a protocol for the game with a cost of $O(n^{.4732})$. We improve 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.

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DeVon Ingram. 2017-12-04. An Upper Bound on the GKS Game via Max Bipartite Matching. https://arxiv.org/abs/1712.01149

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