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… 
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