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Robust Online Monitoring of Signal Temporal Logic

arXiv 1506.08234 ↗First posted 26 Jun 2015eess.SY cs.SYcited by 39

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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.

Key facts. Cited by 39 papers in the map (data through 7 Oct 2026). First posted on arXiv 26 Jun 2015.

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Citing papers per year: 2021: 6; 2022: 7; 2023: 6; 2024: 5; 2025: 3; 2026: 12.

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  1. 2023Forking Uncertainties: Reliable Prediction and Model Predictive Control with Sequence Models via Conformal Risk Controlcited by 19
  2. 2021Learning from Demonstrations using Signal Temporal Logiccited by 17
  3. 2026Detecting Safety Violations Across Many Agent Tracescited by 11
  4. 2024Temporal Logic Specification-Conditioned Decision Transformer for Offline Safe Reinforcement Learningcited by 10
  5. 2021Safety Enhancement for Deep Reinforcement Learning in Autonomous Separation Assurancecited by 8
  6. 2023Multi-Agent Reinforcement Learning Guided by Signal Temporal Logic Specificationscited by 6
  7. 2021Data-driven Design of Context-aware Monitors for Hazard Prediction in Artificial Pancreas Systemscited by 5
  8. 2024Online Safety Analysis for LLMs: a Benchmark, an Assessment, and a Path Forwardcited by 5
  9. 2022Interpretable Fault Diagnosis of Rolling Element Bearings with Temporal Logic Neural Networkcited by 4
  10. 2022A Verification Framework for Certifying Learning-Based Safety-Critical Aviation Systemscited by 3
  11. 2023Synthesizing Efficiently Monitorable Formulas in Metric Temporal Logiccited by 3
  12. 2023Learning-Based Approaches to Predictive Monitoring with Conformal Statistical Guaranteescited by 2
27 more
  1. 2024SpecGuard: Specification Aware Recovery for Robotic Autonomous Vehicles from Physical Attackscited by 2
  2. 2026Learning Gait-Aware Quadruped Locomotion with Temporal Logic Specificationscited by 2
  3. 2025A Framework for Learning Scoring Rules in Autonomous Driving Planning Systemscited by 1
  4. 2026Conformal Signal Temporal Logic for Robust Reinforcement Learning Control: A Case Studycited by 1
  5. 2026Spatiotemporal Robustness of Temporal Logic Tasks using Multi-Objective Reasoningcited by 1
  6. 2021SINGA-Easy: An Easy-to-Use Framework for MultiModal Analysiscited by 0
  7. 2021VisualTextRank: Unsupervised Graph-based Content Extraction for Automating Ad Text to Image Searchcited by 0
  8. 2021Text is NOT Enough: Integrating Visual Impressions into Open-domain Dialogue Generationcited by 0
  9. 2022Discovering Personalized Semantics for Soft Attributes in Recommender Systems using Concept Activation Vectorscited by 0
  10. 2022Reinforced MOOCs Concept Recommendation in Heterogeneous Information Networkscited by 0
  11. 2022An Empirical Analysis of the Use of Real-Time Reachability for the Safety Assurance of Autonomous Vehiclescited by 0
  12. 2022Explanation-Guided Fairness Testing through Genetic Algorithmcited by 0
  13. 2022Using Graph Neural Networks for Program Terminationcited by 0
  14. 2023Tribe or Not? Critical Inspection of Group Differences Using TribalGramcited by 0
  15. 2023Fulfilling Formal Specifications ASAP by Model-free Reinforcement Learningcited by 0
  16. 2024Adaptive Splitting of Reusable Temporal Monitors for Rare Traffic Violationscited by 0
  17. 2024Natural Adversaries: Fuzzing Autonomous Vehicles with Realistic Roadside Object Placementscited by 0
  18. 2025Control Synthesis of Cyber-Physical Systems for Real-Time Specifications through Causation-Guided Reinforcement Learningcited by 0
  19. 2026Validating Generalist Robots with Situation Calculus and STL Falsificationcited by 0
  20. 2025AI Application Operations -- A Socio-Technical Framework for Data-driven Organizationscited by 0
  21. 2026On Tackling Complex Tasks with Reward Machines and Signal Temporal Logicscited by 0
  22. 2026Vision-Based Runtime Monitoring under Varying Specifications using Semantic Latent Representationscited by 0
  23. 2026On the Stability and Realizability of Recurrent Polynomial Surrogate Ternary Logic Gate Networkscited by 0
  24. 2026Learning-enabled Parameter Synthesis for Nonlinear Systems from Signal Temporal Logiccited by 0
  25. 2026Shielding for Higher-Order Safetycited by 0
  26. 2026Reward Machines for Signal Temporal Logiccited by 0
  27. 2026StreamDecisionBench: Evaluating Decisions in Force on Evolving Language Streamscited by 0