# Conformal Prediction for STL Runtime Verification

arXiv: https://arxiv.org/abs/2211.01539 · HTML: https://mlsanity.com/paper/2211.01539/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Nov 2022.

## Built on by (most cited first, 30 of 35)

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- [Distributionally Robust Statistical Verification with Imprecise Neural Networks](https://mlsanity.com/paper/2308.14815/) (2023)
- [Conformal Prediction under Levy-Prokhorov Distribution Shifts: Robustness to Local and Global Perturbations](https://mlsanity.com/paper/2502.14105/) (2025)
- [Data-Driven Reachability Analysis of Stochastic Dynamical Systems with Conformal Inference](https://mlsanity.com/paper/2309.09187/) (2023)
- [How Safe Am I Given What I See? Calibrated Prediction of Safety Chances for Image-Controlled Autonomy](https://mlsanity.com/paper/2308.12252/) (2023)
- [Bridging Dimensions: Confident Reachability for High-Dimensional Controllers](https://mlsanity.com/paper/2311.04843/) (2023)
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- [Recursively Feasible Shrinking-Horizon MPC in Dynamic Environments with Conformal Prediction Guarantees](https://mlsanity.com/paper/2405.10875/) (2024)
- [Conformal Off-Policy Prediction for Multi-Agent Systems](https://mlsanity.com/paper/2403.16871/) (2024)
- [Learning Temporal Logic Predicates from Data with Statistical Guarantees](https://mlsanity.com/paper/2406.10449/) (2024)
- [Physically Interpretable World Models via Weakly Supervised Representation Learning](https://mlsanity.com/paper/2412.12870/) (2024)
- [Safety Monitoring for Learning-Enabled Cyber-Physical Systems in Out-of-Distribution Scenarios](https://mlsanity.com/paper/2504.13478/) (2025)
- [Conformal Prediction for Signal Temporal Logic Inference](https://mlsanity.com/paper/2509.25473/) (2025)
- [Learning-Based Approaches to Predictive Monitoring with Conformal Statistical Guarantees](https://mlsanity.com/paper/2312.01959/) (2023)
- [Watchdogs and Oracles: Runtime Verification Meets Large Language Models for Autonomous Systems](https://mlsanity.com/paper/2511.14435/) (2025)
- [Runtime Monitoring DNN-Based Perception](https://mlsanity.com/paper/2310.03999/) (2023)
- [CoCAI: Copula-based Conformal Anomaly Identification for Multivariate Time-Series](https://mlsanity.com/paper/2507.17796/) (2025)
- [How Safe Will I Be Given What I Saw? Calibrated Prediction of Safety Chances for Image-Controlled Autonomy](https://mlsanity.com/paper/2508.09346/) (2025)
- [Conformal Predictive Monitoring for Multi-Modal Scenarios](https://mlsanity.com/paper/2509.01338/) (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)
- [Towards Safe and Reliable Autonomous Driving: Dynamic Occupancy Set Prediction](https://mlsanity.com/paper/2402.19385/) (2024)
- [Quantitative Predictive Monitoring and Control for Safe Human-Machine Interaction](https://mlsanity.com/paper/2412.13365/) (2024)
- [Monitor and Recover: A Paradigm for Future Research on Distribution Shift in Learning-Enabled Cyber-Physical Systems](https://mlsanity.com/paper/2504.13484/) (2025)

## Abstract (arXiv)

We are interested in predicting failures of cyber-physical systems during their operation. Particularly, we consider stochastic systems and signal temporal logic specifications, and we want to calculate the probability that the current system trajectory violates the specification. The paper presents two predictive runtime verification algorithms that predict future system states from the current observed system trajectory. As these predictions may not be accurate, we construct prediction regions that quantify prediction uncertainty by using conformal prediction, a statistical tool for uncertainty quantification. Our first algorithm directly constructs a prediction region for the satisfaction measure of the specification so that we can predict specification violations with a desired confidence. The second algorithm constructs prediction regions for future system states first, and uses these to obtain a prediction region for the satisfaction measure. To the best of our knowledge, these are the first formal guarantees for a predictive runtime verification algorithm that applies to widely used trajectory predictors such as RNNs and LSTMs, while being computationally simple and making no assumptions on the underlying distribution. We present numerical experiments of an F-16 aircraft and a self-driving car.