Optimal Space Lower Bound for Deterministic Self-Stabilizing Leader Election Algorithms

Given a boolean predicate $\Pi$ on labeled networks (e.g., proper coloring, leader election, etc.), self-stabilizing algorithm for is distributed that can start from any initial configuration of the network (i.e., every node has an arbitrary value assigned to each its variables), and eventually converge satisfying $\Pi$. It known election does not have deterministic using constant-size register at node, i.e., some networks, their nodes must registers whose sizes grow with size $n$ networks. On other hand, it also be solved by $O(\log \log n)$ bits per in $n$-node bounded-degree network. We show this latter space complexity optimal. Specifically, we prove solving use $\Omega(\log n)$-bit In addition, our lower bounds go beyond apply all problems cannot anonymous algorithms.