Various aspects of privacy and safety in many application domains can be assessed based on proper analysis of successive measurements that are collected about a given system. This work is devoted to such issues in the context of timed stochastic discrete event systems (DES) that are modeled with partially observed timed stochastic Petri net models. The first contribution is to introduce a k -step trajectory-observer, which is a construction that captures all possible k -suffixes of the trajectories that are consistent with a given sequence of measurements that has been recorded. When the system behaves according to Markovian dynamics (i.e., all event occurrences are distributed in time with exponential probability density functions), a parallel-like composition of the timed system with the resulting observer is proposed that leads to a Markovian process. The second contribution is to take advantage of the Markovian analysis to compute certain important characteristic times during which the underlying system should satisfy a given property (based on the suffixes of length k of a given trajectory). To illustrate the approach, we consider two particular properties, namely k -suffix language opacity and k -diagnosability, which can be studied in a stochastic timed context using the Markovian trajectory observer.

中文翻译：

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使用马尔可夫轨迹观测器对定时随机离散事件系统进行隐私和安全分析

许多应用领域中隐私和安全的各个方面都可以基于对给定系统收集的连续测量的正确分析进行评估。这项工作致力于在定时随机离散事件系统 (DES) 的上下文中解决此类问题，该系统使用部分观察到的定时随机 Petri 网模型进行建模。第一个贡献是引入 ak 步轨迹观察器，它是一种结构，它捕获轨迹的所有可能的 k 后缀，这些后缀与已记录的给定测量序列一致。当系统按照马尔可夫动力学行为时（即，所有事件的发生均以指数概率密度函数在时间上分布），提出了一种类似平行的定时系统与由此产生的观察者的组合，这导致了马尔可夫过程。第二个贡献是利用马尔可夫分析来计算某些重要的特征时间，在此期间底层系统应该满足给定的属性（基于给定轨迹的长度 k 的后缀）。为了说明该方法，我们考虑两个特定属性，即 k 后缀语言不透明度和 k 可诊断性，它们可以使用马尔可夫轨迹观察器在随机定时上下文中进行研究。