We study a new problem-the wakeup problem-that seems to be fundamental
in distributed computing. We present efficient solutions to the probl
em and show how these solutions can be used to solve the consensus pro
blem, the leader-election problem, and other related problems. The mai
n question we try to answer is ''How much memory is needed to solve th
e wakeup problem?'' We assume a model that captures important properti
es of real systems that have been largely ignored by previous work on
cooperative problems.