Randomized uniform self-stabilizing mutual exclusion

Abstract

A system is self-stabilizing if when started in any configuration it reaches a legal configuration, all subsequent configurations are legal. We present a randomized self-stabilizing mutual exclusion that works on any uniform graphs. It is based on irregularities that have to be present in the graph. Irregularities make random walks and merge on meeting. The number of states is bounded by $\text{o}\text{(Δ}\text{ln}\text{n)}$ where $\text{Δ}$ is the maximal degree and $\text{n}$ is the number of vertices. The protocol is also proof against addition and removal of processors.