  For reaching efficient deterministic synchronous Byzantine agreement upon
partially connected networks, the traditional broadcast primitive is extended
and integrated with a general framework. With this, the Byzantine agreement is
extended to fully connected bipartite networks and some bipartite
bounded-degree networks. The complexity of the Byzantine agreement is lowered
and optimized with the so-called Byzantine-levers under a general system
structure. Some bipartite simulation of the butterfly networks and some finer
properties of bipartite bounded-degree networks are also provided for building
efficient incomplete Byzantine agreement under the same system structure. It
shows that efficient real-world Byzantine agreement systems can be built with
the provided algorithms with sufficiently high system assumption coverage.
Meanwhile, the proposed bipartite solutions can improve the dependability of
the systems in some open, heterogeneous, and even antagonistic environments.
