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 ° OR_n) = Ω((mn)~(1/2)). 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.
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