# Why Formal Monitors Fail: Attack Distribution Entropy as a Coverage Bound for LTL-Based LLM Agent Safety

arXiv: https://arxiv.org/abs/2608.01388 · HTML: https://mlsanity.com/paper/2608.01388/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Agent threats, guardrails and governance, one of 16 directions in LLM agents and tool use.
- Builds on 6 of its 16 references that are in the map.
- First posted on arXiv 2 Aug 2026.

## Placed in

- LLM agents and tool use / [Agent threats, guardrails and governance](https://mlsanity.com/agents/agent-threats-guardrails-and-governance/)

## Builds on (most cited first, 6 of 6)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [AgentSpec: Customizable Runtime Enforcement for Safe and Reliable LLM Agents](https://mlsanity.com/paper/2503.18666/) (2025)
- [Enforcing Temporal Constraints for LLM Agents](https://mlsanity.com/paper/2512.23738/) (2025)
- [AgentSentry: Mitigating Indirect Prompt Injection in LLM Agents via Temporal Causal Diagnostics and Context Purification](https://mlsanity.com/paper/2602.22724/) (2026)
- [Mapping the Exploitation Surface: A 10,000-Trial Taxonomy of What Makes LLM Agents Exploit Vulnerabilities](https://mlsanity.com/paper/2604.04561/) (2026)
- [From LTL to rLTL Monitoring: Improved Monitorability through Robust Semantics](https://mlsanity.com/paper/1807.08203/) (2018)

## Abstract (arXiv)

Runtime safety monitors based on Linear Temporal Logic (LTL) and finite automata (FSA) are increasingly deployed to intercept unsafe tool-call sequences in LLM agents. Yet the same monitor achieves 68-75% attack coverage on some model architectures and near-zero on others, with no explanation from capability scores, training data, or prompt design. We provide the missing theory. We prove that the recall of any fixed-invariant FSA monitor is bounded above by the concentration of the attack distribution: the fraction of attacks covered by the k most frequent trigger-completion patterns. When attacks concentrate (low Shannon entropy), a small fixed invariant set achieves high recall; when they disperse across many structurally distinct patterns (high entropy), no fixed invariant set of tractable size can, regardless of how the invariants were derived. We validate this entropy-coverage bound across eight frontier LLM architectures. GPT-class and DeepSeek backends yield highly concentrated attacks (H ~ 0.24 bits; one pattern covers 96%), explaining 68-75% recall; Gemini variants yield high-entropy distributions (H ~ 2.81 bits; 7 clusters each <= 7%), explaining near-zero recall (6-13%), invariant to architecture-matched retraining. Entropy accounts for 76% of variance in coverage (Pearson r = -0.87, p = 0.005, 95% CI [-0.98, -0.78]), holding under leave-one-out (r in [-0.91, -0.82]). We introduce a pre-deployment entropy test that predicts monitor coverage from a small attack sample, enabling architecture-aware monitor selection before deployment. The bound and test are architecture-agnostic and apply to any FSA-based runtime monitor over discrete action sequences.