Amplification by Read-Once Formulas

@article{Dubiner1997AmplificationBR,
  title={Amplification by Read-Once Formulas},
  author={Moshe Dubiner and Uri Zwick},
  journal={SIAM J. Comput.},
  year={1997},
  volume={26},
  pages={15-38}
}
Moore and Shannon have shown that relays with arbitrarily high reliability can be built from relays with arbitrarily poor reliability. Valiant used similar methods to construct monotone read-once formulas of size $O(n^{\alpha+2})$ (where $\alpha=\log_{\sqrt{5}-1}2\simeq 3.27$) that amplify $(\psi-\frac{1}{n},\psi+\frac{1}{n})$ (where $\psi=(\sqrt{5}-1)/2\simeq0.62$) to $(2^{-n},1-2^{-n})$ and deduced as a consequence the existence of monotone formulas of the same size that compute the majority… 

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