Choreographies prescribe the rendez-vous synchronisation of messages in a system of communicating finite state machines. Such a system is called realisable, if the traces of the prescribed communication coincide with those of the asynchronous system of peers, where the communication channels either use FIFO queues or multiset mailboxes. In a recent article realisability was characterised by two necessary conditions that together are sufficient. A simple consequence is that realisability in the presence of a choreography becomes decidable. In this article we extend this work by generalising choreographies to control-state choreographies, which enable parallelism. We redefine P2P systems on grounds of control-state machines and show that a control-state choreography is equivalent to the rendez-vous compositions of its peers and that language-synchronisability coincides with synchronisability. These results are used to characterise realisability of control-state choreographies. As for the case of FSM-based choreographies we prove two necessary conditions: a sequence condition and a choice condition. Then we also show that these two conditions together are sufficient for the realisability of control-state choreographies.

中文翻译：

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控制状态编排的可实现性

编排规定了有限状态机通信系统中消息的会合同步。如果指定通信的轨迹与对等异步系统的轨迹一致，则这种系统称为可实现，其中通信通道使用 FIFO 队列或多组邮箱。在最近的一篇文章中，可实现性的特点是两个必要条件一起是充分的。一个简单的结果是，在存在编排的情况下，可实现性变得可判定。在本文中，我们通过将编排推广到控制状态编排来扩展这项工作，从而实现并行性。我们基于控制状态机重新定义了 P2P 系统，并表明控制状态编排相当于其对等体的集合点组合，并且语言同步性与同步性一致。这些结果用于表征控制状态编排的可实现性。对于基于 FSM 的编排的情况，我们证明了两个必要条件：序列条件和选择条件。然后我们还表明，这两个条件一起足以实现控制状态编排的可实现性。