LLMs have shown impressive few-shot performance across many tasks. However, they still struggle when it comes to reliably generating complex output structures, such as those required for information extraction. This limitation stems from the fact that LLMs, without fine-tuning, tend to generate free text rather than structures precisely following a specific grammar. In this work, we propose to enrich the decoding with formal grammar constraints. More concretely, given Context-Free Grammar(CFG), our framework ensures that the token generated in each decoding step would lead to a valid continuation compliant with the grammar production rules. This process guarantees the generation of valid sequences. Importantly, our framework can be readily combined with any CFG or decoding algorithm. We demonstrate that the outputs of many NLP tasks can be represented as formal languages, making them suitable for direct use in our framework. We conducted experiments with two challenging tasks involving large alphabets in their grammar (Wikidata entities and relations): information extraction and entity disambiguation. Our results with LLaMA models indicate that grammar-constrained decoding substantially outperforms unconstrained decoding and even competes with task-specific fine-tuned models. These findings suggest that integrating grammar-based constraints during decoding holds great promise in making LLMs reliably produce structured outputs, especially in setting where training data is scarce and fine-tuning is expensive.

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