Our previous work considered detectability of discrete event systems which involves determining the current state and subsequent states of a system based on event observation. We assumed that event observation is static, that is, if an event is observable, then all its occurrences are observable. However, in practical systems such as sensor networks, event observation often needs to be dynamic, that is, the occurrences of same events may or may not be observable, depending on the state of the system. In this paper, we generalize static event observation into dynamic event observation and consider the detectability problem under dynamic event observation. We define four types of detectabilities. To check detectabilities, we construct the observer with exponential complexity. To reduce computational complexity, we can also construct a detector with polynomial complexity to check strong detectabilities. Dynamic event observation can be implemented in two possible ways: a passive observation and an active observation. For the active observation, we discuss how to find minimal event observation policies that preserve four types of detectabilities.

中文翻译：

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具有动态事件观察的离散事件系统的可检测性

我们之前的工作考虑了离散事件系统的可检测性，包括基于事件观察确定系统的当前状态和后续状态。我们假设事件观察是静态的，也就是说，如果一个事件是可观察的，那么它的所有发生都是可观察的。然而，在传感器网络等实际系统中，事件观察往往需要是动态的，即根据系统的状态，相同事件的发生可能会或可能不会被观测到。在本文中，我们将静态事件观察推广到动态事件观察，并考虑了动态事件观察下的可检测性问题。我们定义了四种类型的可检测性。为了检查可检测性，我们构建了具有指数复杂度的观察器。为了降低计算复杂度，我们还可以构建一个具有多项式复杂度的检测器来检查强可检测性。动态事件观察可以通过两种可能的方式实现：被动观察和主动观察。对于主动观察，我们讨论如何找到保留四种可检测性的最小事件观察策略。