This work is set in the context of supervisory control of discrete-event systems under partial observation. Attackers that are able to insert or erase occurrences of particular output symbols can tamper with the supervisor’s observation and by doing so, can lead the controlled system to undesirable states. We consider a scenario with multiple attackers, each one being an element of a set, called the attack set. We also assume that only one of the attackers within an attack set is acting, although we don’t know which one. According to previous results in the literature, a supervisor that enforces a given legal language, regardless of which attacker is acting, can be designed if the legal language is controllable and satisfies a property called P-observability for an attack set. The latter is an extended notion of observability and is related with the supervisor’s ability to always distinguish between outputs that require different control actions, even if the outputs were attacked. We present a new approach for checking if a given language is P-observable for an attack set, by first introducing a visual representation as well as some definitions that capture the attack’s effect. Additionally, we present two algorithms that together allow us to verify if a given language is P-observable for an attack set, when it is represented as an automaton.

这项工作是在部分观察下的离散事件系统的监督控制背景下进行的。能够插入或删除特定输出符号的攻击者可以篡改监督者的观察，并通过这样做可能导致受控系统进入不良状态。我们考虑一个有多个攻击者的场景，每个攻击者都是一个集合的一个元素，称为攻击集. 我们还假设攻击集中只有一个攻击者在行动，尽管我们不知道是哪一个。根据文献中先前的结果，如果法律语言是可控的并且满足称为 P 可观察性的攻击集属性，则可以设计一个强制执行给定法律语言的监督者，而不管攻击者正在采取什么行动。后者是可观察性的扩展概念，与监管者始终区分需要不同控制动作的输出的能力有关，即使输出受到攻击。我们提出了一种新方法，用于检查给定语言对于攻击集是否是 P 可观察的，首先引入视觉表示以及一些捕获攻击效果的定义。此外，