Bounds on the Total Coefficient Size of Nullstellensatz Proofs of the Pigeonhole Principle and the Ordering Principle

05/07/2022

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by   Aaron Potechin, et al.

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In this paper, we investigate the total coefficient size of Nullstellensatz proofs. We show that Nullstellensatz proofs of the pigeonhole principle on n pigeons require total coefficient size 2^Ω(n) and that there exist Nullstellensatz proofs of the ordering principle on n elements with total coefficient size 2^n - n.