  Message propagation is fundamental in constructing distributed systems upon
sparsely connected communication networks. For providing easy message
propagation primitives, the mutual-exclusive propagation (MEP) of one-bit
messages is investigated with a simplified discrete system model. Inspired by
natural propagation systems, efficient self-stabilizing periodic MEP processes
are proposed with the MEP systems. For handling the worst-case scenarios, the
MEP systems are generally analyzed with formal proofs upon arbitrarily
connected networks. It shows that the MEP systems can be stabilized with
arbitrary initial system states within a short bounded time. Meanwhile, the
numeric simulation shows that the propagation errors can be significantly
reduced if the message delays are randomly distributed. Propagation patterns
are also discussed in further deriving finer propagation results in the MEP
systems. It shows that bounded clock drifts and some benign faults can be well
handled in the MEP systems. Featured by its very simple mechanism, the proposed
MEP primitive can be employed as a practical building block of upper-layer
self-stabilizing synchronous systems.
