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Public story · 2026-08-05 · high
A finite-domain version of the problem is solvable, but the proof shows real LLM agents violate the condition that solvability requires.
Why now: The proof carries an August 2026 arXiv ID and gives agent builders a mathematical account, instead of a hunch, for a limit they've mostly argued from intuition.
No algorithm can verify AI agent behavior against a rule set in the general case, a new proof posted to arXiv shows.
It matters for anyone building agents on live data who wants proof, not just testing, that an agent won't take a forbidden action. More compute doesn't close the gap. The paper frames it as a fundamental limit, not a resource problem.
The paper formalizes these systems, agents that call tools against changing data, as Stateful Tool-Enabled Agentic Deployments. It checks their behavior against First-Order CTL specs, the temporal logic formalism used to state what an agent must or must never do.
Restrict the data to a finite domain and the problem becomes solvable, PSPACE-complete instead of undecidable. That only holds if renaming an opaque identifier in the data correspondingly renames which tool calls the agent picks. The paper shows real LLM-driven agents violate that condition.
The authors built a wrapper that enforces the condition anyway. Computing the canonical representation it needs is graph-isomorphism-hard, a problem with no known fast algorithm. Nothing here ships Monday.
Each link below shares sources, entities, or timing with this story.
Simon Willison released LLM / Shared entity: LLM / Shared topic / Earlier coverage / Tension
Linked by a graph relationship (Simon Willison released LLM); both cover LLM; overlapping topics (against, data).
Simon Willison released LLM / Same source domain / Shared topic / Tension
Linked by a graph relationship (Simon Willison released LLM); reported by the same outlet (arxiv.org); overlapping topics (against, agent, data).
Simon Willison released LLM / Shared entity: Monday / Shared topic / Earlier coverage
Linked by a graph relationship (Simon Willison released LLM); both cover Monday; overlapping topics (agent, data).
Simon Willison released LLM / Shared entity: LLM / Shared topic / Earlier coverage
Linked by a graph relationship (Simon Willison released LLM); both cover LLM; overlapping topics (actually, agent).
Linked by a graph relationship (Simon Willison released LLM); both cover LLM; overlapping topics (agent, agentic).
Linked by a graph relationship (Simon Willison released LLM); both cover LLM; overlapping topics (agent, agentic).
Simon Willison released LLM / Shared entity: LLM / Earlier coverage / Tension
Linked by a graph relationship (Simon Willison released LLM); both cover LLM; earlier LLM coverage from 2026-07-27.
Linked by a graph relationship (Simon Willison released LLM); both cover LLM; earlier LLM coverage from 2026-06-18.