A distributed system is self-stabilizing ii it can be started in any p
ossible global state. Once started the system regains its consistency
by itself, without any kind of outside intervention. The self-stabiliz
ation property makes the system tolerant to faults in which processors
exhibit a faulty behavior for a while and then recover spontaneously
in an arbitrary state. When the intermediate period in between one rec
overy and the next faulty period is long enough, the system stabilizes
. A distributed system is uniform if all processors with the same numb
er of neighbors are identical. A distributed system is dynamic if it c
an tolerate addition or deletion of processors and links without reini
tialization. In this work, we study uniform dynamic self-stabilizing p
rotocols for leader election under readwrite atomicity. Our protocols
use randomization to break symmetry. The leader election protocol stab
ilizes in O(Delta D log n) time when the number of the processors is u
nknown and O(Delta D), otherwise. Here Delta denotes the maximal degre
e of a node, D denotes the diameter of the graph and n denotes the num
ber of processors in the graph. We introduce self-stabilizing protocol
s for synchronization that are used as building blocks by the leader-e
lection algorithm. We conclude this work by presenting a simple, unifo
rm, self-stabilizing ranking protocol.