Grammar plays a critical role in natural language processing and text/code generation by enabling the definition of syntax, the creation of parsers, and guiding structured outputs. Although large language models (LLMs) demonstrate impressive capabilities across domains, their ability to infer and generate grammars has not yet been thoroughly explored. In this paper, we aim to study and improve the ability of LLMs for few-shot grammar generation, where grammars are inferred from sets of a small number of positive and negative examples and generated in Backus-Naur Form. To explore this, we introduced a novel dataset comprising 540 structured grammar generation challenges, devised 6 metrics, and evaluated 8 various LLMs against it. Our findings reveal that existing LLMs perform sub-optimally in grammar generation. To address this, we propose an LLM-driven hybrid genetic algorithm, namely HyGenar, to optimize grammar generation. HyGenar achieves substantial improvements in both the syntactic and semantic correctness of generated grammars across LLMs.

Large language model (LLM) agents show promise in an increasing number of domains. In many proposed applications, it is expected that the agent reasons over accumulated experience presented in an input prompt. We propose the OEDD (Operationalize Experience Despite Distraction) corpus, a human-annotator-validated body of scenarios with pre-scripted agent histories where the agent must make a decision based on disparate experiential information in the presence of a distractor. We evaluate three state-of-the-art LLMs (GPT-3.5 Turbo, GPT-4o, and Gemini 1.5 Pro) using a minimal chain-of-thought prompting strategy and observe that when (1) the input context contains over 1,615 tokens of historical interactions, (2) a crucially decision-informing premise is the rightful conclusion over two disparate environment premises, and (3) a trivial, but distracting red herring fact follows, all LLMs perform worse than random choice at selecting the better of two actions. Our code and test corpus are publicly available at: [github.com/sonnygeorge/OEDD](github.com/sonnygeorge/OEDD).