Distinguishing Views in Symmetric Networks: A Tight Lower Bound

TL;DR

This paper establishes a tight lower bound on the depth needed to distinguish node views in symmetric port-labeled networks, showing that views can be identical up to a certain depth despite nodes being different.

Contribution

It proves the existence of networks where node views are indistinguishable up to a specific depth, providing a fundamental limit for view-based symmetry breaking.

Findings

Existence of networks with indistinguishable views up to depth  D\u2212D",

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Abstract

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 $n\geq D\geq 1$, 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 $\Omega(D\log (n/D))$ are identical.