# An Active Learning Approach to the Falsification of Black Box Cyber-Physical Systems

## TL;DR

This paper introduces an active learning-based method to efficiently falsify formal properties of complex black box cyber-physical systems, significantly reducing the number of required model simulations.

## Contribution

It adapts active learning techniques to the falsification of black box models with time-dependent inputs, improving scalability and efficiency.

## Key findings

- Reduced number of model simulations needed for falsification
- Effective on industrial-level automotive benchmark
- Enhanced scalability to complex systems

## Abstract

Search-based testing is widely used to find bugs in models of complex Cyber-Physical Systems. Latest research efforts have improved this approach by casting it as a falsification procedure of formally specified temporal properties, exploiting the robustness semantics of Signal Temporal Logic. The scaling of this approach to highly complex engineering systems requires efficient falsification procedures, which should be applicable also to black box models. Falsification is also exacerbated by the fact that inputs are often time-dependent functions. We tackle the falsification of formal properties of complex black box models of Cyber-Physical Systems, leveraging machine learning techniques from the area of Active Learning. Tailoring these techniques to the falsification problem with time-dependent, functional inputs, we show a considerable gain in computational effort, by reducing the number of model simulations needed. The goodness of the proposed approach is discussed on a challenging industrial-level benchmark from automotive.