# Time-Staging Enhancement of Hybrid System Falsification

## TL;DR

This paper introduces time staging, a method that improves the efficiency of optimization-based falsification of hybrid systems by exploiting the time-causal structure of signals, demonstrated through experiments and theoretical analysis.

## Contribution

The paper proposes a novel time staging approach that enhances hybrid system falsification by incrementally constructing input signals, with supporting theoretical insights.

## Key findings

- Time staging significantly improves falsification performance in certain cases.
- Experimental results confirm the effectiveness of the proposed method.
- Theoretical analysis identifies conditions where time staging is most beneficial.

## Abstract

Optimization-based falsification employs stochastic optimization algorithms to search for error input of hybrid systems. In this paper we introduce a simple idea to enhance falsification, namely time staging, that allows the time-causal structure of time-dependent signals to be exploited by the optimizers. Time staging consists of running a falsification solver multiple times, from one interval to another, incrementally constructing an input signal candidate. Our experiments show that time staging can dramatically increase performance in some realistic examples. We also present theoretical results that suggest the kinds of models and specifications for which time staging is likely to be effective.