Self-stabilizing mutual exclusion on a ring, even if K=N

TL;DR

This paper demonstrates that Dijkstra's self-stabilizing mutual exclusion algorithm on a ring remains effective even when each node has one fewer state than the total number of nodes, challenging previous assumptions.

Contribution

It proves the algorithm's stabilization property under a new condition where states per node are less than the number of nodes, expanding its applicability.

Findings

Algorithm stabilizes with K=N-1 states per node

Contradicts previous belief about state requirements

Extends understanding of self-stabilizing algorithms

Abstract

We show that, contrary to common belief, Dijkstra's self-stabilizing mutual exclusion algorithm on a ring [Dij74,Dij82] also stabilizes when the number of states per node is one less than the number of nodes on the ring.