We study networks of processes that all execute the same finite protocol and communicate synchronously in two different ways: a process can broadcast one message to all other processes or send it to at most one other process. In both cases, if no process can receive the message, it will still be sent. We establish a precise complexity class for two coverability problems with a parameterised number of processes: the state coverability problem and the configuration coverability problem. It is already known that these problems are Ackermann-hard (but decidable) in the general case. We show that when the protocol is Wait-Only, i.e., it has no state from which a process can send and receive messages, the complexity drops to P and PSPACE, respectively.

翻译：我们研究了执行相同有限协议并通过两种不同方式进行同步通信的进程网络：一个进程可以向所有其他进程广播一条消息，或将其发送至最多一个其他进程。在这两种情况下，如果没有进程能接收该消息，它仍会被发送。我们针对两个覆盖性问题（状态覆盖问题与配置覆盖问题）在参数化进程数量下建立了精确的复杂度类别。已知这些通项问题在一般情况下是Ackermann难解（但可判定的）。我们证明当协议为"仅等待"（即不存在某个状态使得进程既能发送又能接收消息）时，复杂度分别降至P和PSPACE。