  Distributed controllers are often necessary for a multi-agent system to
satisfy safety properties such as collision avoidance. Communication and
coordination are key requirements in the implementation of a distributed
control protocol, but maintaining an all-to-all communication topology is
unreasonable and not always necessary. Given a safety objective and a
controller implementation, we consider the problem of identifying when agents
need to communicate with one another and coordinate their actions to satisfy
the safety constraint. We define a coordination-free controllable predecessor
operator that is used to derive a subset of the state space that allows agents
to act independently, without consulting other agents to double check that the
action is safe. Applications are shown for identifying an upper bound on
connection delays and a self-triggered coordination scheme. Examples are
provided which showcase the potential for designers to visually interpret a
system's ability to tolerate delays when initializing a network connection.
