An Efficient Formula Synthesis Method with Past Signal Temporal Logic

In this work, we propose a novel method to find temporal properties that lead to the unexpected behaviors from labeled dataset. We express these properties in past time Signal Temporal Logic (ptSTL). First, we present a novel approach for finding parameters of a template ptSTL formula, which extends the results on monotonicity based parameter synthesis. The proposed method optimizes a given monotone criteria while bounding an error. Then, we employ the parameter synthesis method in an iterative unguided formula synthesis framework. In particular, we combine optimized formulas iteratively to describe the causes of the labeled events while bounding the error. We illustrate the proposed framework on two examples.