# Time Robustness in MTL and Expressivity in Hybrid System Falsification (Extended Version)

arXiv: https://arxiv.org/abs/1505.06307 · HTML: https://mlsanity.com/paper/1505.06307/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 May 2015.

## Built on by (most cited first, 8 of 8)

- [Part-X: A Family of Stochastic Algorithms for Search-Based Test Generation with Probabilistic Guarantees](https://mlsanity.com/paper/2110.10729/) (2021)
- [STL Robustness Risk over Discrete-Time Stochastic Processes](https://mlsanity.com/paper/2104.01503/) (2021)
- [Uncertainty-Aware Signal Temporal Logic Inference](https://mlsanity.com/paper/2105.11545/) (2021)
- [Reinforcement Learning with Formal Performance Metrics for Quadcopter Attitude Control under Non-nominal Contexts](https://mlsanity.com/paper/2107.12942/) (2021)
- [A Neurosymbolic Approach to the Verification of Temporal Logic Properties of Learning enabled Control Systems](https://mlsanity.com/paper/2303.05394/) (2023)
- [Spatiotemporal Robustness of Temporal Logic Tasks using Multi-Objective Reasoning](https://mlsanity.com/paper/2603.29868/) (2026)
- [Scaling Learning based Policy Optimization for Temporal Logic Tasks by Controller Network Dropout](https://mlsanity.com/paper/2403.15826/) (2024)
- [LogSTOP: Temporal Scores over Prediction Sequences for Matching and Retrieval](https://mlsanity.com/paper/2510.06512/) (2025)

## Abstract (arXiv)

Building on the work by Fainekos and Pappas and the one by Donze and Maler, we introduce AvSTL, an extension of metric interval temporal logic by averaged temporal operators. Its expressivity in capturing both space and time robustness helps solving falsification problems, (i.e. searching for a critical path in hybrid system models); it does so by communicating a designer's intention more faithfully to the stochastic optimization engine employed in a falsification solver. We also introduce a sliding window-like algorithm that keeps the cost of computing truth/robustness values tractable.