Distinguishing views in symmetric networks: A tight lower bound

The view of a node in a port-labeled network is an infinite tree encoding all walks in the network originating from this node. We prove that for any integers n≥D≥1n≥D≥1, there exists a port-labeled network with at most n nodes and diameter at most D   which contains a pair of nodes whose (infinite) views are different, but whose views truncated to depth Ω(Dlog⁡(n/D))Ω(Dlog⁡(n/D)) are identical.