Towards Better Separation between Deterministic and Randomized Query Complexity

@article{Mukhopadhyay2015TowardsBS,
  title={Towards Better Separation between Deterministic and Randomized Query Complexity},
  author={Sagnik Mukhopadhyay and Swagato Sanyal},
  journal={Electronic Colloquium on Computational Complexity (ECCC)},
  year={2015},
  volume={22},
  pages={107}
}
We show that there exists a Boolean function F which observes the following separations among deterministic query complexity (D(F)), randomized zero error query complexity (R0(F)) and randomized one-sided error query complexity (R1(F)): R1(F) = Õ( √ D(F)) and R0(F) = Õ(D(F)) 3/4. This refutes the conjecture made by Saks and Wigderson that for any Boolean function f , R0( f ) = Ω(D( f ))0.753... This also shows widest separation between R1( f ) and D( f ) for any Boolean function. The function F… CONTINUE READING

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