In our previous work, we investigated detectability of discrete event systems, which is defined as the ability to determine the current and subsequent states of a system based on observation. For different applications, we defined four types of detectabilities: (weak) detectability, strong detectability, (weak) periodic detectability, and strong periodic detectability. In this paper, we extend our results in three aspects. (1) We extend detectability from deterministic systems to nondeterministic systems. Such a generalization is necessary because there are many systems that need to be modeled as nondeterministic discrete event systems. (2) We develop polynomial algorithms to check strong detectability. The previous algorithms are based on observer whose construction is of exponential complexity, while the new algorithms are based on a new automaton called detector. (3) We extend detectability to D-detectability. While detectability requires determining the exact state of a system, D-detectability relaxes this requirement by asking only to distinguish certain pairs of states. With these extensions, the theory on detectability of discrete event systems becomes more applicable in solving many practical problems.

中文翻译：

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离散事件系统的广义可检测性

在我们之前的工作中，我们研究了离散事件系统的可检测性，它被定义为基于观察确定系统当前和后续状态的能力。针对不同的应用，我们定义了四种可探测性：（弱）可探测性、强可探测性、（弱）周期性可探测性和强周期性可探测性。在本文中，我们从三个方面扩展了我们的结果。(1) 我们将可检测性从确定性系统扩展到非确定性系统。这种概括是必要的，因为有许多系统需要建模为非确定性离散事件系统。(2) 我们开发多项式算法来检查强可检测性。以前的算法基于观察者，其构造具有指数复杂性，而新算法基于称为检测器的新自动机。(3) 我们将可检测性扩展到 D 可检测性。虽然可检测性需要确定系统的确切状态，但 D 可检测性通过仅要求区分某些状态对来放宽这一要求。通过这些扩展，离散事件系统的可检测性理论更适用于解决许多实际问题。