A Composition Theorem via Conflict Complexity

@article{Sanyal2018ACT,
  title={A Composition Theorem via Conflict Complexity},
  author={Swagato Sanyal},
  journal={Electronic Colloquium on Computational Complexity (ECCC)},
  year={2018},
  volume={25},
  pages={14}
}
  • Swagato Sanyal
  • Published 2018 in Electronic Colloquium on Computational Complexity
Let R(·) stand for the bounded-error randomized query complexity. We show that for any relation f ⊆ {0, 1}×S and partial Boolean function g ⊆ {0, 1}×{0, 1}, R1/3(f ◦g) = Ω(R4/9(f)· √ R1/3(g)). Independently of us, Gavinsky, Lee and Santha [3] proved this result. By an example demonstrated in their work, this bound is optimal. We prove our result by introducing a novel complexity measure called the conflict complexity of a partial Boolean function g, denoted by χ(g), which may be of independent… CONTINUE READING