Deterministic , Constant Space , Self - Stabilizing Leader Electionon Uniform

We consider the problem of electing a leader on a ring of nameless processors by de-terministic and self-stabilizing protocols. A processor can read the state of its neighbors (and its own state) to determine if it is enabled. A central demon (scheduler) picks an enabled processor to make an atomic move. In an atomic move, the processor changes to a new state which is a function of its old state and the states of its two neighbors. It is well known that no deterministic protocol exists if n, the size of the ring is composite. If the size of the ring is a prime, surprisingly, there is a deterministic leader election protocol. In this paper, we present a protocol for bidirectional rings of prime size. Our protocol is deterministic, uses constant space and is self-stabilizing, in O(n 2) steps.