Multiparty Communication Complexity of Collision Finding
For complexity theorists, this provides a significantly stronger lower bound for a natural propositional proof system, advancing understanding of proof complexity.
The paper proves a lower bound on the multiparty communication complexity of collision finding, which implies an exponential lower bound on tree-like cutting-planes proofs of the bit pigeonhole principle, improving previous bounds from 2^{Ω(√n)} to 2^{n^{1-o(1)}}.
We prove an $Ω(n^{1-1/k} \log k \ /2^k)$ lower bound on the $k$-party number-in-hand communication complexity of collision-finding. This implies a $2^{n^{1-o(1)}}$ lower bound on the size of tree-like cutting-planes proofs of the bit pigeonhole principle, a compact and natural propositional encoding of the pigeonhole principle, improving on the best previous lower bound of $2^{Ω(\sqrt{n})}$.