# An Efficient Formula Synthesis Method with Past Signal Temporal Logic

## TL;DR

This paper introduces a new method for synthesizing temporal properties in past time Signal Temporal Logic to identify causes of unexpected behaviors in datasets, combining parameter optimization and iterative formula synthesis.

## Contribution

It presents a novel approach for parameter synthesis of ptSTL formulas and integrates it into an iterative framework for effective formula generation.

## Key findings

- Successfully applied to two example cases
- Effectively identifies causes of labeled events
- Bounds error while optimizing parameters

## Abstract

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.

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Source: https://tomesphere.com/paper/1904.07828