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TR05-053 | 4th May 2005 00:00
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#### Lower bounds for Lovasz-Schrijver systems and beyond follow from multiparty communication complexity

**Abstract:**
We prove that an \omega(log^3 n) lower bound for the three-party number-on-the-forehead (NOF) communication complexity of the set-disjointness function implies an n^\omega(1) size lower bound for tree-like Lovasz-Schrijver systems that refute unsatisfiable CNFs. More generally, we prove that an n^\Omega(1) lower bound for the (k+1)-party NOF communication complexity of set-disjointness implies a 2^{n^\Omega(1)} size lower bound for all tree-like proof systems whose formulas are degree k polynomial inequalities.