Clique Is Hard on Average for Sherali-Adams with Bounded Coefficients
arxiv(2024)
摘要
We prove that Sherali-Adams with polynomially bounded coefficients requires
proofs of size n^Ω(d) to rule out the existence of 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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