In this paper, we propose a new property of of an automaton with respect to a given cover on its set of marker states. This property the standard nonblocking property by capturing the practical requirement that every subset (i.e. cell) of marker states can be reached within a prescribed number of steps from any reachable state and following any trajectory of the system. Accordingly, we formulate a new problem of quantitatively nonblocking supervisory control, and characterize its solvability in terms of a new concept of quantitative language completability. It is proven that there exists the unique supremal quantitatively completable sublanguage of a given language, and we develop an effective algorithm to compute the supremal sublanguage. Finally, combining with the algorithm of computing the supremal controllable sublanguage, we design an algorithm to compute the maximally permissive solution to the formulated quantitatively nonblocking supervisory control problem.

中文翻译：

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离散事件系统的定量无阻塞监控


在本文中，我们提出了自动机关于其标记状态集的给定覆盖的新属性。该属性通过捕获实际要求来实现标准的非阻塞属性，即标记状态的每个子​​集（即单元）可以在从任何可到达状态的规定数量的步骤内到达并遵循系统的任何轨迹。因此，我们提出了一个新的定量无阻塞监督控制问题，并根据定量语言可完成性的新概念来表征其可解性。证明了给定语言存在唯一的最高定量可完成子语言，并且我们开发了一种有效的算法来计算最高子语言。最后，结合计算最高可控子语言的算法，我们设计了一种算法来计算公式化的定量无阻塞监督控制问题的最大许可解。