Sum of squares bounds for the ordering principle

Aaron Potechin

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arXiv · 1812.01163

Sum of squares bounds for the ordering principle

Aaron Potechin

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Abstract

In this paper, we analyze the sum of squares hierarchy (SOS) on the ordering principle on $n$ elements. We prove that degree $O(\sqrt{n}log(n))$ SOS can prove the ordering principle. We then show that this upper bound is essentially tight by proving that for any $\epsilon > 0$, SOS requires degree $\Omega(n^{\frac{1}{2} - \epsilon})$ to prove the ordering principle on $n$ elements.

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Aaron Potechin. 2018-12-04. Sum of squares bounds for the ordering principle. https://arxiv.org/abs/1812.01163

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