# Monotone Circuit Lower Bounds from Robust Sunflowers

@article{Cavalar2020MonotoneCL, title={Monotone Circuit Lower Bounds from Robust Sunflowers}, author={B. P. Cavalar and Mrinal Kumar and Benjamin Rossman}, journal={Electron. Colloquium Comput. Complex.}, year={2020}, volume={27}, pages={181} }

Robust sunflowers are a generalization of combinatorial sunflowers that have applications in monotone circuit complexity, DNF sparsification, randomness extractors, and recent advances on the Erdős-Rado sunflower conjecture. The recent breakthrough of Alweiss, Lovett, Wu and Zhang gives an improved bound on the maximum size of a $w$-set system that excludes a robust sunflower. In this paper, we use this result to obtain an $\exp(n^{1/2-o(1)})$ lower bound on the monotone circuit size of an…

## 9 Citations

Sunflower Theorems in Monotone Circuit Complexity

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