  For reaching fast and efficient self-stabilizing Byzantine pulse
synchronization (SSBPS) upon the bounded-delay message-passing networks, we
consider the peaceable SSBPS problem where the resource occupation in the
stabilized system is required to be as sparse as possible and the stabilization
of the system is required to be as fast as possible. To solve it, the decoupled
absorption process and emergency process are investigated under a general
framework. The constant-time two-stage absorption process and more than one
kind of emergency process are provided in integrating the merits of temporal
trails, approximate agreements, deterministic and randomized Byzantine
agreements, and self-stabilizing protocols. With this, not only SSBPS but
self-stabilizing Byzantine clock synchronization can be fast established and
efficiently maintained. In the optimal-resilient basic solutions, the
deterministic linear stabilization time and the stabilized resource occupation
are all optimized to those of the underlying primitives, which is optimal in
the presence of Byzantine faults under the classical static adversary. In the
hybrid solutions, faster stabilization can be expected with a worst-case
deterministic stabilization time. In all solutions, the stabilized resource
occupation is at most at the order of approximate agreement, which is a good
property in considering real-world ultra-high-reliable hard-real-time
applications where pulse synchronization is expected to be established before
all upper-layer functions and to be efficiently maintained when the upper-layer
functions are in service.
