Natural-language tasking of embodied agents is rarely just goal specification: users also impose constraints that must persist while the world changes. Code-generating LLM agents can produce plausible behaviors for such instructions, but their free-form programs provide no stable object to verify, compose with new constraints, or repair from a failing trace. We present CEDAR, a counterexample-guided framework that grounds instructions as regular languages over environment event traces. CEDAR uses a language model for semantic judgments and execution traces for correction, then represents both skills and specifications as deterministic finite automata. This turns constraints into executable finite-state objects: a learned skill can be intersected with a learned sleep at night or stay in this biome specification, yielding a controller that enforces the learned constraint by construction rather than by repeated prompting. In Minecraft, with the same simulator/API observations available to a program-generating baseline, CEDAR maintains temporal and spatial constraints that the baseline fails to preserve and amortizes reuse of learned skills, reducing cumulative LLM queries. These results suggest that regular languages offer a practical verification layer between natural-language instructions and embodied-agent policies.
Chenyu Zhou, Qiliang Jiang, Shuning Wu +1cs.CR cs.LG
Hard-constrained sequential decision systems have no certified way to spend the test-time compute of modern AI: executing the multi-step drafts of a learned policy or a frozen LLM forfeits the feasibility guarantee a trusted solver provides, while invoking the solver at every step forfeits the speed the AI offers. Certificate-Gated Prefix Acceptance (CGPA) closes this gap with a certified speculative-execution contract for untrusted AI agents: a trusted verifier rejects constraint-violating transitions exactly, a conformally calibrated value boundary gates the longest low-cost prefix within a per-segment regret budget, and the rest defers to the solver, so safety, regret, and speed decouple by construction. The contract drives every untrusted proposal source - adversarial drafters and six heterogeneous frozen LLMs (including a 12B model that violates constraints in 98% of direct rollouts) - to zero applied violations; a certificate-aware learned boundary, conformally calibrated, drives mean regret three orders of magnitude below unguarded acceptance, to within sampling noise of the stepwise oracle (95% CI spanning zero), and under calendar shift a learned proposal source overtakes it on 15 of 18 held-out days. On a deployment-scale unit-commitment instance it turns a frozen 8B LLM into a 2.96x per-episode wall-clock speedup at 2.1% regret, outpacing the domain heuristic (1.79x) and a safe receding-horizon baseline (1.07x): the more capable the untrusted source, the faster the certified system, at guarantees that never change.