Opacity is a property expressing whether a system may reveal its secret to a passive observer (an intruder) who knows the structure of the system but has a limited observation of its behavior. Several notions of opacity have been studied, including current-state opacity, K-step opacity, and infinite-step opacity. We study K-step opacity that generalizes both current-state opacity and infinite-step opacity, and asks whether the intruder cannot decide, at any time, whether or when the system was in a secret state during the last K observable steps. We design a new algorithm deciding K-step opacity the complexity of which is lower than that of existing algorithms and that does not depend on K. We then compare K-step opacity with other opacity notions and provide new transformations among the notions that do not use states that are neither secret nor non-secret (neutral states) and that are polynomial with respect to both the size of the system and the binary encoding of K.

中文翻译：

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离散事件系统中的 K 步不透明度：验证、复杂性和关系

不透明度是一种属性，表示系统是否可以向了解系统结构但对其行为的观察有限的被动观察者（入侵者）透露其秘密。已经研究了几种不透明度的概念，包括当前状态不透明度、K 步不透明度和无限步不透明度。我们研究了 K 步不透明度，它概括了当前状态不透明度和无限步不透明度，并询问入侵者是否无法随时决定系统在最后 K 个可观察步骤中是否或何时处于秘密状态。我们设计了一种新算法决定 K 步不透明度，其复杂度低于现有算法，并且不依赖于 K。