🤖 AI Summary
本文提出了一种解决精确被动学习Metric Interval Temporal Logic（MITL）的方法，通过将时间学习问题转换为非时间问题，并合成精确的时间约束来嵌入到布尔原子命题中。
📝 Abstract
Automated mining of formal specifications is vital for verifying real-time systems. However, existing passive learning approaches remain restricted to deterministic specifications or limited fragments of Timed Regular Expressions (TRE). To our knowledge, this paper presents the first framework to tackle \emph{precise} passive learning for an expressive timed logic, \emph{Metric Interval Temporal Logic} (MITL) without relying on predefined templates or restricted logic fragments.
Our approach formally reduces the timed learning problem into a scalable untimed one. By identifying quantitative timing differences between positive and negative traces, we synthesise precise timed constraints and inject them as new Boolean atomic propositions. This embeds timing into the alphabet, delegating the complex formula evaluation to highly optimised, off-the-shelf untimed LTL tools.
Crucially, our framework is complete, guaranteeing a separating specification can always be found. We evaluate our implementation across several benchmarks, demonstrating the effectiveness of our approach.