We revisit the problem of synchronisability for communicating automata, i.e., whether the language of send messages for an asynchronous system is the same as the language of send messages with a synchronous communication. The un/decidability of the problem depends on the specific asynchronous semantics considered as well as the topology (the communication flow) of the system. Synchronisability is known to be undecidable under the peer-to-peer semantics, while it is still an open problem for mailbox communication. The problem was shown to be decidable for ring topologies. In this paper, we show that when generalising to automata with accepting states, synchronisability is undecidable under the mailbox semantics, this result is obtained by resorting to the Post Correspondence problem. In an attempt to solve the specific problem where all states are accepting, we also show that synchronisability is decidable for tree topologies (where, as well as for rings, peer-to-peer coincides with mailbox semantics). We also discuss synchronisability for multitrees in the mailbox setting.

翻译：我们重新审视通信自动机的可同步性问题，即异步系统的发送消息语言是否与同步通信下的发送消息语言相同。该问题的可判定性/不可判定性取决于所考虑的特定异步语义以及系统的拓扑结构（通信流）。已知在点对点语义下可同步性是不可判定的，而对于邮箱通信，这仍是一个未解决的问题。该问题已被证明在环形拓扑下是可判定的。本文中，我们证明当推广到具有接受状态的自动机时，邮箱语义下的可同步性是不可判定的，这一结果通过借助波斯特对应问题获得。在尝试解决所有状态均为接受状态这一特定问题时，我们还证明了在树形拓扑下（与环形拓扑一样，点对点语义与邮箱语义在此重合）可同步性是可判定的。我们亦讨论了邮箱设置下多树结构的可同步性。