# Robust Online Monitoring of Signal Temporal Logic

arXiv: https://arxiv.org/abs/1506.08234 · HTML: https://mlsanity.com/paper/1506.08234/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jun 2015.

## Built on by (most cited first, 30 of 39)

- [Forking Uncertainties: Reliable Prediction and Model Predictive Control with Sequence Models via Conformal Risk Control](https://mlsanity.com/paper/2310.10299/) (2023)
- [Learning from Demonstrations using Signal Temporal Logic](https://mlsanity.com/paper/2102.07730/) (2021)
- [Detecting Safety Violations Across Many Agent Traces](https://mlsanity.com/paper/2604.11806/) (2026)
- [Temporal Logic Specification-Conditioned Decision Transformer for Offline Safe Reinforcement Learning](https://mlsanity.com/paper/2402.17217/) (2024)
- [Safety Enhancement for Deep Reinforcement Learning in Autonomous Separation Assurance](https://mlsanity.com/paper/2105.02331/) (2021)
- [Multi-Agent Reinforcement Learning Guided by Signal Temporal Logic Specifications](https://mlsanity.com/paper/2306.06808/) (2023)
- [Online Safety Analysis for LLMs: a Benchmark, an Assessment, and a Path Forward](https://mlsanity.com/paper/2404.08517/) (2024)
- [Data-driven Design of Context-aware Monitors for Hazard Prediction in Artificial Pancreas Systems](https://mlsanity.com/paper/2104.02545/) (2021)
- [Interpretable Fault Diagnosis of Rolling Element Bearings with Temporal Logic Neural Network](https://mlsanity.com/paper/2204.07579/) (2022)
- [A Verification Framework for Certifying Learning-Based Safety-Critical Aviation Systems](https://mlsanity.com/paper/2205.04590/) (2022)
- [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)
- [SpecGuard: Specification Aware Recovery for Robotic Autonomous Vehicles from Physical Attacks](https://mlsanity.com/paper/2408.15200/) (2024)
- [Learning Gait-Aware Quadruped Locomotion with Temporal Logic Specifications](https://mlsanity.com/paper/2607.00442/) (2026)
- [A Framework for Learning Scoring Rules in Autonomous Driving Planning Systems](https://mlsanity.com/paper/2502.11352/) (2025)
- [Conformal Signal Temporal Logic for Robust Reinforcement Learning Control: A Case Study](https://mlsanity.com/paper/2602.14322/) (2026)
- [Spatiotemporal Robustness of Temporal Logic Tasks using Multi-Objective Reasoning](https://mlsanity.com/paper/2603.29868/) (2026)
- [SINGA-Easy: An Easy-to-Use Framework for MultiModal Analysis](https://mlsanity.com/paper/2108.02572/) (2021)
- [VisualTextRank: Unsupervised Graph-based Content Extraction for Automating Ad Text to Image Search](https://mlsanity.com/paper/2108.02725/) (2021)
- [Text is NOT Enough: Integrating Visual Impressions into Open-domain Dialogue Generation](https://mlsanity.com/paper/2109.05778/) (2021)
- [Discovering Personalized Semantics for Soft Attributes in Recommender Systems using Concept Activation Vectors](https://mlsanity.com/paper/2202.02830/) (2022)
- [Reinforced MOOCs Concept Recommendation in Heterogeneous Information Networks](https://mlsanity.com/paper/2203.11011/) (2022)
- [An Empirical Analysis of the Use of Real-Time Reachability for the Safety Assurance of Autonomous Vehicles](https://mlsanity.com/paper/2205.01419/) (2022)
- [Explanation-Guided Fairness Testing through Genetic Algorithm](https://mlsanity.com/paper/2205.08335/) (2022)
- [Using Graph Neural Networks for Program Termination](https://mlsanity.com/paper/2207.14648/) (2022)
- [Tribe or Not? Critical Inspection of Group Differences Using TribalGram](https://mlsanity.com/paper/2303.09664/) (2023)
- [Fulfilling Formal Specifications ASAP by Model-free Reinforcement Learning](https://mlsanity.com/paper/2304.12508/) (2023)
- [Adaptive Splitting of Reusable Temporal Monitors for Rare Traffic Violations](https://mlsanity.com/paper/2405.15771/) (2024)
- [Natural Adversaries: Fuzzing Autonomous Vehicles with Realistic Roadside Object Placements](https://mlsanity.com/paper/2409.10562/) (2024)
- [Control Synthesis of Cyber-Physical Systems for Real-Time Specifications through Causation-Guided Reinforcement Learning](https://mlsanity.com/paper/2510.07715/) (2025)

## Abstract (arXiv)

Signal Temporal Logic (STL) is a formalism used to rigorously specify requirements of cyberphysical systems (CPS), i.e., systems mixing digital or discrete components in interaction with a continuous environment or analog com- ponents. STL is naturally equipped with a quantitative semantics which can be used for various purposes: from assessing the robustness of a specification to guiding searches over the input and parameter space with the goal of falsifying the given property over system behaviors. Algorithms have been proposed and implemented for offline computation of such quantitative semantics, but only few methods exist for an online setting, where one would want to monitor the satisfaction of a formula during simulation. In this paper, we formalize a semantics for robust online monitoring of partial traces, i.e., traces for which there might not be enough data to decide the Boolean satisfaction (and to compute its quantitative counterpart). We propose an efficient algorithm to compute it and demonstrate its usage on two large scale real-world case studies coming from the automotive domain and from CPS education in a Massively Open Online Course (MOOC) setting. We show that savings in computationally expensive simulations far outweigh any overheads incurred by an online approach.