A new rewrite method for proving convergence of self-stabilizing systems

Abstract

In the framework of self-stabilizing systems, the convergence proof is generally done by exhibiting a measure that strictly decreases until a legitimate configuration is reached. The discovery of such a measure is very specific and requires a deep understanding of the studied transition system. In contrast we propose here a simple method for proving convergence, which regards self-stabilizing systems as string rewrite systems, and adapts a procedure initially designed by Dershowitz for proving termination of string rewrite systems.