# On-Line Monitoring for Temporal Logic Robustness

arXiv: https://arxiv.org/abs/1408.0045 · HTML: https://mlsanity.com/paper/1408.0045/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jul 2014.

## Built on by (most cited first, 15 of 15)

- [Model-Free Reinforcement Learning for Optimal Control of MarkovDecision Processes Under Signal Temporal Logic Specifications](https://mlsanity.com/paper/2109.13377/) (2021)
- [Temporal Logic Specification-Conditioned Decision Transformer for Offline Safe Reinforcement Learning](https://mlsanity.com/paper/2402.17217/) (2024)
- [Part-X: A Family of Stochastic Algorithms for Search-Based Test Generation with Probabilistic Guarantees](https://mlsanity.com/paper/2110.10729/) (2021)
- [Interpretable Fault Diagnosis of Rolling Element Bearings with Temporal Logic Neural Network](https://mlsanity.com/paper/2204.07579/) (2022)
- [Safe Model-based Control from Signal Temporal Logic Specifications Using Recurrent Neural Networks](https://mlsanity.com/paper/2103.15938/) (2021)
- [Synthesizing Efficiently Monitorable Formulas in Metric Temporal Logic](https://mlsanity.com/paper/2310.17410/) (2023)
- [Learning-Based Approaches to Predictive Monitoring with Conformal Statistical Guarantees](https://mlsanity.com/paper/2312.01959/) (2023)
- [Deep Reinforcement Learning Based Networked Control with Network Delays for Signal Temporal Logic Specifications](https://mlsanity.com/paper/2108.01317/) (2021)
- [Shielded Reinforcement Learning Under Dynamic Temporal Logic Constraints](https://mlsanity.com/paper/2603.17152/) (2026)
- [Spatiotemporal Robustness of Temporal Logic Tasks using Multi-Objective Reasoning](https://mlsanity.com/paper/2603.29868/) (2026)
- [Provably Correct Controller Synthesis of Switched Stochastic Systems with Metric Temporal Logic Specifications: A Case Study on Power Systems](https://mlsanity.com/paper/2103.14264/) (2021)
- [Safety Verification and Navigation for Autonomous Vehicles based on Signal Temporal Logic Constraints](https://mlsanity.com/paper/2409.10689/) (2024)
- [Control Synthesis of Cyber-Physical Systems for Real-Time Specifications through Causation-Guided Reinforcement Learning](https://mlsanity.com/paper/2510.07715/) (2025)
- [Specification-Aware Distribution Shaping for Robotics Foundation Models](https://mlsanity.com/paper/2603.17969/) (2026)
- [Vision-Based Runtime Monitoring under Varying Specifications using Semantic Latent Representations](https://mlsanity.com/paper/2605.13923/) (2026)

## Abstract (arXiv)

In this paper, we provide a Dynamic Programming algorithm for on-line monitoring of the state robustness of Metric Temporal Logic specifications with past time operators. We compute the robustness of MTL with unbounded past and bounded future temporal operators MTL over sampled traces of Cyber-Physical Systems. We implemented our tool in Matlab as a Simulink block that can be used in any Simulink model. We experimentally demonstrate that the overhead of the MTL robustness monitoring is acceptable for certain classes of practical specifications.