Cyber-physical systems often encompass complex concurrent behavior with timing constraints and probabilistic failures on demand. The analysis whether such systems with probabilistic timed behavior ad-here to a given specification is essential. When the states of the system can be represented by graphs, the rule-based formalism of Probabilistic Timed Graph Transformation Systems (PTGTSs) can be used to suitably capture structure dynamics as well as probabilistic and timed behavior of the system. The model checking support for PTGTSs w.r.t. properties specified using Probabilistic Timed Computation Tree Logic (PTCTL) has been already presented. Moreover, for timed graph-based runtime monitoring, Metric Temporal Graph Logic (MTGL) has been developed for stating metric temporal properties on identified subgraphs and their structural changes over time. In this paper, we (a) extend MTGL to the Probabilistic Metric Temporal Graph Logic (PMTGL) by allowing for the specification of probabilistic properties, (b) adapt our MTGL satisfaction checking approach to PTGTSs, and (c) combine the approaches for PTCTL model checking and MTGL satisfaction checking to obtain a Bounded Model Checking (BMC) approach for PMTGL. In our evaluation, we apply an implementation of our BMC approach in AutoGraph to a running example.

中文翻译：

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概率度量时间图逻辑

网络物理系统通常包含复杂的并发行为，具有时间限制和按需概率故障。分析此类具有概率定时行为的系统是否符合给定规范至关重要。当系统的状态可以用图表示时，概率定时图转换系统 (PTGTS) 的基于规则的形式可用于适当地捕获结构动力学以及系统的概率和定时行为。已经介绍了对使用概率定时计算树逻辑 (PTCTL) 指定的 PTGTS wrt 属性的模型检查支持。此外，对于基于定时图的运行时监控，已经开发了度量时间图逻辑 (MTGL) 来说明已识别子图的度量时间属性及其随时间的结构变化。在本文中，我们 (a) 通过允许概率属性的规范将 MTGL 扩展到概率度量时间图逻辑 (PMTGL)，(b) 将我们的 MTGL 满意度检查方法应用于 PTGTS，以及 (c) 结合 PTCTL 的方法模型检查和 MTGL 满意度检查以获得 PMTGL 的有界模型检查 (BMC) 方法。在我们的评估中，我们将 AutoGraph 中 BMC 方法的实现应用于运行示例。