A monitoring algorithm is trace-length independent if its space consumption does not depend on the number of events processed. The analysis of many monitoring algorithms has aimed at establishing their trace-length independence. But a monitor’s space consumption can depend on characteristics of the trace other than its size. We put forward the stronger notion of event-rate independence, where a monitor’s space usage does not depend on the event rate, i.e., the number of events in a fixed time unit. This property is critical for monitoring voluminous streams of events with a high arrival rate. We propose a new algorithm for metric temporal logic (MTL) that is almost event-rate independent, where “almost” denotes a logarithmic dependence on the event rate: the algorithm must store the event rate as a number. Afterwards, we investigate more expressive logics. In particular, we extend linear dynamic logic with past operators and metric features. The resulting metric dynamic logic (MDL) offers the quantitative temporal conveniences of MTL while increasing its expressiveness. We show how to modify our MTL algorithm in a modular way, yielding an almost event-rate independent monitor for MDL. Finally, we compare our algorithms with traditional monitoring approaches, providing empirical evidence that almost event-rate independence matters in practice.

中文翻译：

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几乎事件率独立监控

如果监视算法的空间消耗不依赖于处理的事件数，则它与跟踪长度无关。许多监控算法的分析旨在建立它们的跟踪长度独立性。但是监视器的空间消耗可能取决于轨迹的特征而不是其大小。我们提出了更强的事件率独立性概念，其中监视器的空间使用不依赖于事件率，即固定时间单位内的事件数。此属性对于监视具有高到达率的大量事件流至关重要。我们提出了一种新的度量时间逻辑 (MTL) 算法，该算法几乎与事件率无关，其中“几乎”表示对事件率的对数依赖性：该算法必须将事件率存储为数字。然后，我们研究更具表现力的逻辑。特别是，我们使用过去的运算符和度量特征扩展了线性动态逻辑。由此产生的度量动态逻辑 (MDL) 提供了 MTL 的定量时间便利，同时增加了其表达能力。我们展示了如何以模块化方式修改我们的 MTL 算法，为 MDL 生成一个几乎与事件率无关的监视器。最后，我们将我们的算法与传统的监控方法进行了比较，提供了在实践中几乎与事件率无关的经验证据。为 MDL 生成一个几乎与事件率无关的监视器。最后，我们将我们的算法与传统的监控方法进行了比较，提供了在实践中几乎事件率独立性很重要的经验证据。为 MDL 生成一个几乎与事件率无关的监视器。最后，我们将我们的算法与传统的监控方法进行了比较，提供了在实践中几乎事件率独立性很重要的经验证据。