Sum of squares bounds for the total ordering principle
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In this paper, we analyze the sum of squares hierarchy (SOS) on the total ordering principle on n elements. We show that degree Õ(√(n)) SOS can prove the total ordering principle so in this setting SOS is considerably more powerful than resolution, polynomial calculus, and the Sherali-Adams hierarchy. We also show superconstant degree SOS lower bounds which we believe can be improved to degree Ω̃(√(n)).
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