  The ``Pulse Synchronization'' problem can be loosely described as targeting
to invoke a recurring distributed event as simultaneously as possible at the
different nodes and with a frequency that is as regular as possible. This
target becomes surprisingly subtle and difficult to achieve when facing both
transient and permanent failures. In this paper we present an algorithm for
pulse synchronization that self-stabilizes while at the same time tolerating a
permanent presence of Byzantine faults. The Byzantine nodes might incessantly
try to de-synchronize the correct nodes. Transient failures might throw the
system into an arbitrary state in which correct nodes have no common notion
what-so-ever, such as time or round numbers, and can thus not infer anything
from their own local states upon the state of other correct nodes. The
presented algorithm grants nodes the ability to infer that eventually all
correct nodes will invoke their pulses within a very short time interval of
each other and will do so regularly.
  Pulse synchronization has previously been shown to be a powerful tool for
designing general self-stabilizing Byzantine algorithms and is hitherto the
only method that provides for the general design of efficient practical
protocols in the confluence of these two fault models. The difficulty, in
general, to design any algorithm in this fault model may be indicated by the
remarkably few algorithms resilient to both fault models. The few published
self-stabilizing Byzantine algorithms are typically complicated and sometimes
converge from an arbitrary initial state only after exponential or super
exponential time.
