Direct Sums in Randomized Communication Complexity

@article{Barak2009DirectSI,
  title={Direct Sums in Randomized Communication Complexity},
  author={Boaz Barak and Mark Braverman and Xi Chen and Anup Rao},
  journal={Electronic Colloquium on Computational Complexity (ECCC)},
  year={2009},
  volume={16},
  pages={44}
}
We prove a direct sum theorem for randomized communication complexity. Ignoring logarithmic factors, our results show that: • Computing n copies of a function requires √n times the communication. • For average case complexity, given any distribution μ on inputs, computing n copies of the function on n independent inputs sampled according to μ requires √ n times the communication for computing one copy. • If μ is a product distribution, computing n copies on n independent inputs sampled… CONTINUE READING