We investigate the problem of synthesizing dynamic masks that preserve the infinite-step opacity in the context of discrete-event systems. Dynamic mask is an information acquisition mechanism that controls the observability of the system's events dynamically online, e.g., by turning sensors on/off. A system equipped with a dynamic mask is said to be infinite-step opaque if an outside intruder that can access all acquired information can never infer that the system was at some secret state for any specific previous instant. Existing works on the dynamic mask synthesis problem can only preserve the current-state opacity. However, synthesizing dynamic masks for the infinite-step opacity, which is stronger than the current-state opacity, is much more challenging. The main reason is that the delayed information is involved in this problem and whether or not a current secret can be revealed depends on sensing decisions to be synthesized in the future. In this paper, a new type of information state is proposed to capture all the delayed information in the infinite-step opacity synthesis problem. An effective algorithm is then presented to solve the synthesis problem, which extends existing dynamic mask synthesis techniques from the current-state opacity to infinite-step opacity. Additionally, an information-state-reduction-based approach is proposed to further mitigate the computational complexity of the synthesis procedure. Finally, we discuss how to generalize our results to a class properties with delayed information including infinite-step K-anonymity and infinite-step indistinguishability.

中文翻译：

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无限级不透明度动态蒙版的合成


我们研究了合成动态掩模的问题，该掩模在离散事件系统的背景下保持无限步长的不透明度。动态掩码是一种信息获取机制，可动态在线控制系统事件的可观察性，例如通过打开/关闭传感器。如果可以访问所有已获取信息的外部入侵者永远无法推断出系统在任何特定的先前时刻处于某种秘密状态，则配备动态掩码的系统被称为无限步不透明。关于动态掩模合成问题的现有工作只能保留当前状态的不透明度。然而，合成比当前状态不透明度更强的无限步不透明度的动态蒙版更具挑战性。主要原因是这个问题涉及延迟信息，当前秘密能否被泄露取决于未来要合成的感知决策。本文提出了一种新型信息状态来捕获无限步不透明合成问题中的所有延迟信息。然后提出了一种有效的算法来解决合成问题，将现有的动态掩模合成技术从当前状态不透明度扩展到无限步不透明度。此外，提出了一种基于信息状态缩减的方法来进一步减轻合成过程的计算复杂性。最后，我们讨论如何将我们的结果推广到具有延迟信息的类属性，包括无限步 K-匿名性和无限步不可区分性。