# Learning Context-Free Grammars for Grammar-Constrained Decoding via Declarative Agentic Programming with Guarantees

arXiv: https://arxiv.org/abs/2608.05493 · HTML: https://mlsanity.com/paper/2608.05493/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in General LLM agent frameworks and benchmarks, one of 16 directions in LLM agents and tool use.
- Builds on 15 of its 37 references that are in the map.
- First posted on arXiv 6 Aug 2026.

## Placed in

- LLM agents and tool use / [General LLM agent frameworks and benchmarks](https://mlsanity.com/agents/general-llm-agent-frameworks-and-benchmarks/)

## Builds on (most cited first, 15 of 15)

- [MemGPT: Towards LLMs as Operating Systems](https://mlsanity.com/paper/2310.08560/) (2023)
- [DIN-SQL: Decomposed In-Context Learning of Text-to-SQL with Self-Correction](https://mlsanity.com/paper/2304.11015/) (2023)
- [Grammar-Constrained Decoding for Structured NLP Tasks without Finetuning](https://mlsanity.com/paper/2305.13971/) (2023)
- [ProofNet: Autoformalizing and Formally Proving Undergraduate-Level Mathematics](https://mlsanity.com/paper/2302.12433/) (2023)
- [A Survey on LLM-based Code Generation for Low-Resource and Domain-Specific Programming Languages](https://mlsanity.com/paper/2410.03981/) (2024)
- [Solver-Aided Verification of Policy Compliance in Tool-Augmented LLM Agents](https://mlsanity.com/paper/2603.20449/) (2026)
- [Bridging LLM Planning Agents and Formal Methods: A Case Study in Plan Verification](https://mlsanity.com/paper/2510.03469/) (2025)
- [Synthetic Programming Elicitation for Text-to-Code in Very Low-Resource Programming and Formal Languages](https://mlsanity.com/paper/2406.03636/) (2024)
- [Learning Highly Recursive Input Grammars](https://mlsanity.com/paper/2108.13340/) (2021)
- [Regexes are Hard: Decision-making, Difficulties, and Risks in Programming Regular Expressions](https://mlsanity.com/paper/2303.02555/) (2023)
- [Early Diagnosis of Wasted Computation in Multi-Agent LLM Systems via Failure-Aware Observability](https://mlsanity.com/paper/2606.01365/) (2026)
- [Synthesizing Program Input Grammars](https://mlsanity.com/paper/1608.01723/) (2016)
- [HyGenar: An LLM-Driven Hybrid Genetic Algorithm for Few-Shot Grammar Generation](https://mlsanity.com/paper/2505.16978/) (2025)
- [Doc2Spec: Synthesizing Formal Programming Specifications from Natural Language via Grammar Induction](https://mlsanity.com/paper/2602.04892/) (2026)
- [Fast Deterministic Black-box Context-free Grammar Inference](https://mlsanity.com/paper/2308.06163/) (2023)

## Abstract (arXiv)

Language models (LMs) are increasingly used to interact with external services via programs written in domain-specific languages (DSLs). Unfortunately, since DSLs are often low-resource and esoteric, LMs frequently produce syntactically invalid programs in these languages. Grammar-constrained decoding can eliminate such failures, but requires syntactic constraints. These are usually in the form of a context-free grammar for the target language, an artifact that is hard to come by for third-party DSLs. In this work, we define an agent, called Autogrammar, that automatically learns context-free grammars from documentation and execution data. Autogrammar is formalized as a Kripke structure whose nondeterministic choices are resolved by a language model, enabling declarative control of agent behavior via linear temporal logic constraints. We evaluate four versions of Autogrammar on three DSLs (i.e., Amazon CloudWatch Logs Insights, Dynatrace Query Language, and Datadog Search Syntax) and find that it generates grammars that achieve near perfect precision on unseen data; that temporal restrictions reduce execution time by 3.8x without incurring statistically-significant loss in precision; that execution data is crucial while documentation is dispensable; and that grammar-constrained decoding using Autogrammar-generated grammars significantly improves end-to-end LM performance on eight out of ten real tasks, matching or exceeding the performance of a professionally-maintained grammar. In comparison, the context-free grammars generated by existing LM baselines and a state-of-the-art formal technique perform significantly worse over the same evaluation.