# 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}
}```
• Published 7 December 2020
• Mathematics, Computer Science
• Electron. Colloquium Comput. Complex.
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…
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