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Creators/Authors contains: "Risse, Kilian"

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  1. ; ; (, 2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS))
    We prove that unary Sherali-Adams requires proofs of size n^Ω(d) to rule out the existence o f an n^Θ(1)-clique in Erdős-Rényi random graphs whose maximum clique is of size d ≤ 2log n. This lower bound is tight up to the multiplicative constant in the exponent. We obtain this result by introducing a technique inspired by pseudo-calibration which may be of independent interest. The technique involves defining a measure on monomials that precisely captures the contribution of a monomial to a refutation . This measure intuitively captures progress and should have further applications in proof complexity. 
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