A Direct Product Theorem for Discrepancy

@article{Lee2008ADP,
  title={A Direct Product Theorem for Discrepancy},
  author={Troy Lee and Adi Shraibman and R. Spalek},
  journal={2008 23rd Annual IEEE Conference on Computational Complexity},
  year={2008},
  pages={71-80}
}
Discrepancy is a versatile bound in communication complexity which can be used to show lower bounds in randomized, quantum, and even weakly-unbounded error models of communication. We show an optimal product theorem for discrepancy, namely that for any two Boolean functions f, g, disc(f odot g)=thetas(disc(f) disc(g)). As a consequence we obtain a strong direct product theorem for distributional complexity, and direct sum theorems for worst-case complexity, for bounds shown by the discrepancy… Expand
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