To avoid the state-space explosion problem, a set of supervisors may be synthesized using divide and conquer strategies, like modular or multilevel synthesis. Unfortunately, these supervisors may be conflicting, meaning that even though they are individually non-blocking, they are together blocking. Abstraction-based compositional nonblocking verification of extended finite automata provides means to verify whether a set of models is nonblocking. In case of a blocking system, a coordinator can be synthesized to resolve the blocking. This paper presents a framework for compositional coordinator synthesis for discrete-event systems modeled as extended finite automata. The framework allows for synthesis of a coordinator on the abstracted system in case compositional verification identifies the system to be blocking. As the abstracted system may use notions not present in the original model, like renamed events, the synthesized coordinator is refined such that it will be nonblocking, controllable, and maximally permissive for the original system. For each abstraction, it is shown how this refinement can be performed. It turns out that for the presented set of abstractions the coordinator refinement is straightforward.

中文翻译：

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扩展有限自动机的组合协调器综合

为了避免状态空间爆炸问题，可以使用分而治之的策略来合成一组监督器，例如模块化或多级综合。不幸的是，这些监督者可能是相互冲突的，这意味着即使他们单独不阻塞，他们一起阻塞。扩展有限自动机的基于抽象的组合非阻塞验证提供了验证一组模型是否非阻塞的方法。在阻塞系统的情况下，可以合成协调器来解决阻塞。本文提出了一个用于建模为扩展有限自动机的离散事件系统的组合协调器合成框架。该框架允许在抽象系统上合成协调器，以防组合验证识别出要阻塞的系统。由于抽象系统可能会使用原始模型中不存在的概念，例如重命名的事件，因此对合成协调器进行了改进，使其对原始系统无阻塞、可控且最大程度地允许。对于每个抽象，都显示了如何执行这种细化。事实证明，对于所呈现的一组抽象，协调器细化很简单。