We prove that the proof system OBDD(and, weakening) is not automatable unless P = NP. The proof is based upon the celebrated result of Atserias and Muller [FOCS 2019] about the hardness of automatability for resolution. The heart of the proof is lifting with a multi-output indexing gadget from resolution ... more >>>

We prove several results concerning the communication complexity of a collision-finding problem, each of which has applications to the complexity of cutting-plane proofs, which make inferences based on integer linear inequalities.

In particular, we prove an $\Omega(n^{1-1/k} \log k \ /2^k)$ lower bound on the $k$-party number-in-hand communication complexity of ... more >>>