Group communication is the basic infrastructure for implementing fault-tolerant replicated servers. While group communication is well understood in the context of static groups (in which the membership does not change), current specifications of dynamic group communication (in which processes can join and leave groups during the computation) have not yet reached the same level of maturity.

The paper proposes new specifications -- in the primary partition model -- for dynamic reliable broadcast (simply called "reliable multicast"), dynamic atomic broadcast (simply called "atomic multicast") and group membership. In the special case of a static system, the new specifications are identical to the well known static specifications. Interestingly, not only are these new specifications "syntactically" close to the static specifications, but they are also "semantically" close to the dynamic specifications proposed in the literature. We believe that this should contribute to clarify a topic that has always been difficult to understand by outsiders.

Finally, the paper shows how to solve atomic multicast, group membership and reliable broadcast. The solution of atomic multicast is close to the (static) atomic broadcast solution based on reduction to consensus. Group membership is solved using atomic multicast. Reliable multicast can be efficiently solved by relying on a thrifty generic multicast algorithm.