We present a runtime verification framework that allows on-line monitoring of past-time Metric Temporal Logic (ptMTL) specifications in a discrete time setting. We design observer algorithms for the time-bounded modalities of ptMTL, which take advantage of the highly parallel nature of hardware designs. The algorithms can be translated into efficient hardware blocks, which are designed for reconfigurability, thus, facilitate applications of the framework in both a prototyping and a post-deployment phase of embedded real-time systems. We provide formal correctness proofs for all presented observer algorithms and analyze their time and space complexity. For example, for the most general operator considered, the time-bounded Since operator, we obtain a time complexity that is doubly logarithmic both in the point in time the operator is executed and the operator’s time bounds. This result is promising with respect to a self-contained, non-interfering monitoring approach that evaluates real-time specifications in parallel to the system-under-test. We implement our framework on a Field Programmable Gate Array platform and use extensive simulation and logic synthesis runs to assess the benefits of the approach in terms of resource usage and operating frequency.

中文翻译：

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嵌入式实时系统的运行时验证

我们提出了一个运行时验证框架，允许在离散时间设置中在线监控过去时间度量时间逻辑 (ptMTL) 规范。我们为 ptMTL 的限时模式设计了观察者算法，它利用了硬件设计的高度并行性。这些算法可以转化为高效的硬件模块，这些模块专为可重构性而设计，从而促进了该框架在嵌入式实时系统的原型设计和部署后阶段的应用。我们为所有提出的观察者算法提供形式正确性证明，并分析它们的时间和空间复杂度。例如，对于所考虑的最通用的运算符，限时自运算符，我们获得了一个时间复杂度，它在操作符执行的时间点和操作符的时间范围内都是双对数的。这个结果对于独立的、无干扰的监控方法来说是有希望的，该方法可以与被测系统并行评估实时规范。我们在现场可编程门阵列平台上实施我们的框架，并使用广泛的模拟和逻辑综合运行来评估该方法在资源使用和操作频率方面的优势。