Almost Two State Self Stabilizing Synchronous Ring

A self stabilizing distributed system is a network of state machines which, regardless of its initial global state, once started will regain its consistency by itself in a nite number of steps. Two are the main issues in the design of a self-stabilizing system: stabilization time and memory requirements. In this paper we present an almost two state self stabilizing unidirectional system solving the mutual exclusion problem where the machines are interconnected in a ring topology and the system is synchronous i.e. and an upper bound k on the relative machine speed is known; the system has an O(n) stabilization time where n is the number of machines in the ring. Furthermore it is shown that the only one two state solution for asynchronous rings to our knowledge, the probabilistic system presented in Fla94], self stabilizes only in partially synchronous systems where the upper bound k exists but is unknown and that for this solution convergence time and token circulation delay cannot be bounded.