# Testing Equality in Networks

Yesterday, I went to an interesting talk by Klim Efremenko about testing equality in networks. The talk was based on his joint paper with Noga Alon and Benny Sudakov. The basic problem is as follows. Suppose there is a network with \(k\) nodes, and each node \(v\) has an input in the form of an \(n\)-bit string \(M_v \in \{0, 1\}^n\). All of the nodes in the network want to verify that all of their strings are equal, i.e., that \(M_v = M_u\) for all…