Balanced boolean functions that can be evaluated so that every input bit is unlikely to be read

@inproceedings{Benjamini2005BalancedBF,
  title={Balanced boolean functions that can be evaluated so that every input bit is unlikely to be read},
  author={Itai Benjamini and Oded Schramm and David Bruce Wilson},
  booktitle={STOC},
  year={2005}
}
A Boolean function of <i>n</i> bits is balanced if it takes the value 1 with probability 1⁄2. We exhibit a balanced Boolean function with a randomized evaluation procedure (with probability 0 of making a mistake) so that on uniformly random inputs, no input bit is read with probability more than Θ(<i>n</i><sup>-1/2</sup>√ log <i>n</i>). We construct a… CONTINUE READING