Abstract
We prove a simple, nearly tight lower bound on the approximate degree of the two-level AND-OR tree using symmetrization arguments. Specifically, we show that ˜ deg(AND m ˆ OR n ) = ˜ Ω(√ mn ). We prove this lower bound via reduction to the OR function through a series of symmetrization steps, in contrast to most other proofs that involve formulating approximate degree as a linear program [6, 10, 21]. Our proof also demonstrates the power of a symmetrization technique involving Laurent polynomials (polynomials with negative exponents) that was previously introduced by Aaronson et al. [2].
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have