Memory requirements for silent stabilization

A stabilizing algorithm is silent if starting from an arbitrary state it converges to a global state after which the values stored in the communication registers are fixed. Many silent stabilizing algorithms have appeared in the literature. In this paper we show that there cannot exist constant memory silent stabilizing algorithms for finding the centers of a graph, electing a leader, and constructing a spanning tree. We demonstrate a lower bound of Ω(log n) bits per communication register for each of the above tasks.