Exponential lower bounds for cutting planes and Res(⊕) on binary clique formulas for random dense graphs, with polynomial randomized communication complexity for falsified clause finding.
Lower bounds for Lov´ asz–Schrijver systems and beyond follow from multiparty communication complexity.SIAM Journal on Computing, 37(3):845–869
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Explicit families of CNF formulas exist such that tree-like semantic Frege refutations with line size s(n) require superpolynomial length for most formulas in the family, for s(n) in a broad range from nearly quadratic to subexponential in n.
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Average-Case Hardness of Binary-Encoded Clique in Proof and Communication Complexity
Exponential lower bounds for cutting planes and Res(⊕) on binary clique formulas for random dense graphs, with polynomial randomized communication complexity for falsified clause finding.
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Superpolynomial Length Lower Bounds for Tree-Like Semantic Proof Systems with Bounded Line Size
Explicit families of CNF formulas exist such that tree-like semantic Frege refutations with line size s(n) require superpolynomial length for most formulas in the family, for s(n) in a broad range from nearly quadratic to subexponential in n.