Shield Synthesis: Runtime Enforcement for Reactive Systems
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Abstract (arXiv)
Scalability issues may prevent users from verifying critical properties of a complex hardware design. In this situation, we propose to synthesize a "safety shield" that is attached to the design to enforce the properties at run time. Shield synthesis can succeed where model checking and reactive synthesis fail, because it only considers a small set of critical properties, as opposed to the complex design, or the complete specification in the case of reactive synthesis. The shield continuously monitors the input/output of the design and corrects its erroneous output only if necessary, and as little as possible, so other non-critical properties are likely to be retained. Although runtime enforcement has been studied in other domains such as action systems, reactive systems pose unique challenges where the shield must act without delay. We thus present the first shield synthesis solution for reactive hardware systems and report our experimental results. This is an extended version of [5], featuring an additional appendix.
Key facts. Cited by 41 papers in the map (data through 7 Oct 2026). First posted on arXiv 12 Jan 2015.
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Citing papers per year: 2022: 4; 2023: 5; 2024: 12; 2025: 4; 2026: 16.
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- 2022Online Shielding for Reinforcement Learningcited by 19
- 2023Runtime Monitoring of Dynamic Fairness Propertiescited by 17
- 2024Formally Verifying Deep Reinforcement Learning Controllers with Lyapunov Barrier Certificatescited by 15
- 2024Verification-Guided Shielding for Deep Reinforcement Learningcited by 13
- 2024Shield Synthesis for LTL Modulo Theoriescited by 12
- 2022Dynamic Shielding for Reinforcement Learning in Black-Box Environmentscited by 11
- 2022Correct-by-Construction Runtime Enforcement in AI -- A Surveycited by 10
- 2022Automata Learning meets Shieldingcited by 9
- 2023Shielded Reinforcement Learning for Hybrid Systemscited by 8
- 2024Leveraging Approximate Model-based Shielding for Probabilistic Safety Guarantees in Continuous Environmentscited by 5
- 2023Approximate Model-Based Shielding for Safe Reinforcement Learningcited by 4
- 2024Efficient Shield Synthesis via State-Space Transformationcited by 4
29 more
- 2026Sovereign Assurance Boundary: Certificate-Bound Admission for Agentic Infrastructurecited by 4
- 2023Safety Shielding under Delayed Observationcited by 3
- 2024Optimal Transport-Assisted Risk-Sensitive Q-Learningcited by 3
- 2024Learning-Based Shielding for Safe Autonomy under Unknown Dynamicscited by 3
- 2023Approximate Shielding of Atari Agents for Safe Explorationcited by 2
- 2024Shielded Deep Reinforcement Learning for Complex Spacecraft Taskingcited by 2
- 2024Predictable and Performant Reactive Synthesis Modulo Theories via Functional Synthesiscited by 2
- 2024Neural Control and Certificate Repair via Runtime Monitoringcited by 2
- 2026Semantic Quorum Assurance: Collective Certification for Non-Deterministic AI Infrastructurecited by 2
- 2026Sovereign Execution Broker: Enforcing Certificate-Bound Authority in Agentic Control Planescited by 2
- 2024Think Smart, Act SMARL! Analyzing Probabilistic Logic Shields for Multi-Agent Reinforcement Learningcited by 1
- 2025ScenicProver: A Framework for Compositional Probabilistic Verification of Learning-Enabled Systemscited by 1
- 2026Safe Reinforcement Learning via Recovery-based Shielding with Gaussian Process Dynamics Modelscited by 1
- 2026Easy-to-Use Shielding for Reinforcement Learningcited by 1
- 2026What Can Be Enforced? A Theory of Certified Runtime Safety for Tool-Using Agentscited by 1
- 2026Compiling Sufficient Governance Context from Declared Losses and Reachable States: Exact Observation-Contract Synthesis with Cardinality and Cost Objectivescited by 1
- 2024MORTAR: A Model-based Runtime Action Repair Framework for AI-enabled Cyber-Physical Systemscited by 0
- 2025Efficient Dynamic Shielding for Parametric Safety Specificationscited by 0
- 2025Formal Verification of Neural Certificates Done Dynamicallycited by 0
- 2025Adaptive GR(1) Specification Repair for Liveness-Preserving Shielding in Reinforcement Learningcited by 0
- 2026COOL-MC: Verifying and Explaining RL Policies for Platelet Inventory Managementcited by 0
- 2026NeuroNL2LTL: A Neurosymbolic Framework for Natural Language Translation of Linear Temporal Logiccited by 0
- 2026Explainably Safe Reinforcement Learningcited by 0
- 2026Shielded Analysis: Certification and Characterization of Defensibility in Systems under Adversarial Interactioncited by 0
- 2026Is Your Agent Playing Dead? Deployed LLM Agents Exhibit Constraint-Evasive Fabrication and Thanatosiscited by 0
- 2026Cycle-Consistent Neural Explanation of Formal Verification Certificatescited by 0
- 2026Shielding for Higher-Order Safetycited by 0
- 2026DeFiFlowBench: Benchmarking and Improving Safe Executability in Natural-Language DeFi Workflow Synthesiscited by 0
- 2026Making Agents More Consistent: Skills Should Form Habits for Repeat Taskscited by 0
- 2026Compiling Sufficient Governance Context from Declared Losses and Reachable States: Exact Observation-Contract Synthesis with Cardinality and Cost Objectives22 Sep 2026
- 2026Making Agents More Consistent: Skills Should Form Habits for Repeat Tasks21 Sep 2026
- 2026DeFiFlowBench: Benchmarking and Improving Safe Executability in Natural-Language DeFi Workflow Synthesis10 Sep 2026
- 2026Shielding for Higher-Order Safety4 Aug 2026
- 2026What Can Be Enforced? A Theory of Certified Runtime Safety for Tool-Using Agents24 Jul 2026
- 2026Cycle-Consistent Neural Explanation of Formal Verification Certificates23 Jun 2026
- 2026Sovereign Execution Broker: Enforcing Certificate-Bound Authority in Agentic Control Planes18 Jun 2026
- 2026Is Your Agent Playing Dead? Deployed LLM Agents Exhibit Constraint-Evasive Fabrication and Thanatosis12 Jun 2026
- 2026Shielded Analysis: Certification and Characterization of Defensibility in Systems under Adversarial Interaction11 Jun 2026
- 2026Sovereign Assurance Boundary: Certificate-Bound Admission for Agentic Infrastructure10 Jun 2026
- 2026Semantic Quorum Assurance: Collective Certification for Non-Deterministic AI Infrastructure6 Jun 2026
- 2026Explainably Safe Reinforcement Learning3 Jun 2026
29 more
- 2026Easy-to-Use Shielding for Reinforcement Learning2 Jun 2026
- 2026NeuroNL2LTL: A Neurosymbolic Framework for Natural Language Translation of Linear Temporal Logic20 May 2026
- 2026COOL-MC: Verifying and Explaining RL Policies for Platelet Inventory Management2 Mar 2026
- 2026Safe Reinforcement Learning via Recovery-based Shielding with Gaussian Process Dynamics Models12 Feb 2026
- 2025Adaptive GR(1) Specification Repair for Liveness-Preserving Shielding in Reinforcement Learning4 Nov 2025
- 2025ScenicProver: A Framework for Compositional Probabilistic Verification of Learning-Enabled Systems4 Nov 2025
- 2025Formal Verification of Neural Certificates Done Dynamically16 Jul 2025
- 2025Efficient Dynamic Shielding for Parametric Safety Specifications28 May 2025
- 2024Neural Control and Certificate Repair via Runtime Monitoring17 Dec 2024
- 2024Think Smart, Act SMARL! Analyzing Probabilistic Logic Shields for Multi-Agent Reinforcement Learning7 Nov 2024
- 2024Learning-Based Shielding for Safe Autonomy under Unknown Dynamics7 Oct 2024
- 2024MORTAR: A Model-based Runtime Action Repair Framework for AI-enabled Cyber-Physical Systems7 Aug 2024
- 2024Efficient Shield Synthesis via State-Space Transformation29 Jul 2024
- 2024Predictable and Performant Reactive Synthesis Modulo Theories via Functional Synthesis12 Jul 2024
- 2024Optimal Transport-Assisted Risk-Sensitive Q-Learning17 Jun 2024
- 2024Verification-Guided Shielding for Deep Reinforcement Learning10 Jun 2024
- 2024Shield Synthesis for LTL Modulo Theories6 Jun 2024
- 2024Formally Verifying Deep Reinforcement Learning Controllers with Lyapunov Barrier Certificates22 May 2024
- 2024Shielded Deep Reinforcement Learning for Complex Spacecraft Tasking8 Mar 2024
- 2024Leveraging Approximate Model-based Shielding for Probabilistic Safety Guarantees in Continuous Environments1 Feb 2024
- 2023Shielded Reinforcement Learning for Hybrid Systems28 Aug 2023
- 2023Approximate Model-Based Shielding for Safe Reinforcement Learning27 Jul 2023
- 2023Safety Shielding under Delayed Observation5 Jul 2023
- 2023Runtime Monitoring of Dynamic Fairness Properties8 May 2023
- 2023Approximate Shielding of Atari Agents for Safe Exploration21 Apr 2023
- 2022Online Shielding for Reinforcement Learning4 Dec 2022
- 2022Automata Learning meets Shielding4 Dec 2022
- 2022Correct-by-Construction Runtime Enforcement in AI -- A Survey30 Aug 2022
- 2022Dynamic Shielding for Reinforcement Learning in Black-Box Environments27 Jul 2022
- 2022Online Shielding for Reinforcement Learningcited by 19
- 2023Runtime Monitoring of Dynamic Fairness Propertiescited by 17
- 2024Formally Verifying Deep Reinforcement Learning Controllers with Lyapunov Barrier Certificatescited by 15
- 2024Verification-Guided Shielding for Deep Reinforcement Learningcited by 13
- 2024Shield Synthesis for LTL Modulo Theoriescited by 12
- 2022Dynamic Shielding for Reinforcement Learning in Black-Box Environmentscited by 11
- 2022Correct-by-Construction Runtime Enforcement in AI -- A Surveycited by 10
- 2022Automata Learning meets Shieldingcited by 9
- 2023Shielded Reinforcement Learning for Hybrid Systemscited by 8
- 2024Leveraging Approximate Model-based Shielding for Probabilistic Safety Guarantees in Continuous Environmentscited by 5
- 2023Approximate Model-Based Shielding for Safe Reinforcement Learningcited by 4
- 2024Efficient Shield Synthesis via State-Space Transformationcited by 4
12 most cited of 38 All 38 (JSON)
- 2026Compiling Sufficient Governance Context from Declared Losses and Reachable States: Exact Observation-Contract Synthesis with Cardinality and Cost Objectives22 Sep 2026
- 2026Making Agents More Consistent: Skills Should Form Habits for Repeat Tasks21 Sep 2026
- 2026DeFiFlowBench: Benchmarking and Improving Safe Executability in Natural-Language DeFi Workflow Synthesis10 Sep 2026
- 2026Shielding for Higher-Order Safety4 Aug 2026
- 2026Cycle-Consistent Neural Explanation of Formal Verification Certificates23 Jun 2026
- 2026Shielded Analysis: Certification and Characterization of Defensibility in Systems under Adversarial Interaction11 Jun 2026
- 2026Sovereign Assurance Boundary: Certificate-Bound Admission for Agentic Infrastructure10 Jun 2026
- 2026Semantic Quorum Assurance: Collective Certification for Non-Deterministic AI Infrastructure6 Jun 2026
- 2026Explainably Safe Reinforcement Learning3 Jun 2026
- 2026Easy-to-Use Shielding for Reinforcement Learning2 Jun 2026
- 2026NeuroNL2LTL: A Neurosymbolic Framework for Natural Language Translation of Linear Temporal Logic20 May 2026
- 2026COOL-MC: Verifying and Explaining RL Policies for Platelet Inventory Management2 Mar 2026
12 newest of 38 All 38 (JSON)