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Lower Bounding the AND-OR Tree via Symmetrization

Published:21 January 2021Publication History
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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(ANDm ˆ ORn) = ˜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].

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