Separations in Query Complexity Based on Pointer Functions

@article{Ambainis2015SeparationsIQ,
  title={Separations in Query Complexity Based on Pointer Functions},
  author={Andris Ambainis and Kaspars Balodis and Aleksandrs Belovs and Troy Lee and Miklos Santha and Juris Smotrovs},
  journal={Electronic Colloquium on Computational Complexity (ECCC)},
  year={2015},
  volume={22},
  pages={98}
}
In 1986, Saks and Wigderson conjectured that the largest separation between deterministic and zero-error randomized query complexity for a total Boolean function is given by the function <i>f</i> on <i>n</i> = 2<i><sup>k</sup></i> bits defined by a complete binary tree of NAND gates of depth <i>k</i>, which achieves <i>R</i><sub>0</sub>(<i>f</i>) = <i>O</i>(<i>D</i>(<i>f</i>)<sup>0.7537…</sup>). We show that this is false by giving an example of a total Boolean function <i>f</i> on <i>n</i… CONTINUE READING
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