Extensive LLM applications demand efficient structured generations, particularly for LR(1) grammars, to produce outputs in specified formats (e.g., JSON). Existing methods primarily parse LR(1) grammars into a pushdown automaton (PDA), leading to runtime execution overhead for context-dependent token processing, especially inefficient under large inference batches.To address these issues, we propose Pre³ that exploits deterministic pushdown automata (DPDA) to optimize the constrained LLM decoding efficiency.First, by **pre**computing **pre**fix-conditioned edges during the **pre**processing, Pre³ enables ahead-of-time edge analysis and thus makes parallel transition processing possible.Futher, leveraging the prefix-conditioned edges, Pre³ introduces a novel approach that transforms LR(1) transition graphs into DPDA, eliminating the need for runtime path exploration and achieving edge transitions with minimal overhead.Pre³ can be seamlessly integrated into standard LLM inference frameworks, improving time per output token (TPOT) by up to 40% and throughput by up to 36% in our experiments. Our code is available at https://github.com/ModelTC/lightllm.

This paper studies speculative reasoning task on real-world knowledge graphs (KG) that contain both false negative issue (i.e., potential true facts being excluded) and false positive issue (i.e., unreliable or outdated facts being included). State-of-the-art methods fall short in the speculative reasoning ability, as they assume the correctness of a fact is solely determined by its presence in KG, making them vulnerable to false negative/positive issues. The new reasoning task is formulated as a noisy Positive-Unlabeled learning problem. We propose a variational framework, namely nPUGraph, that jointly estimates the correctness of both collected and uncollected facts (which we call label posterior) and updates model parameters during training. The label posterior estimation facilitates speculative reasoning from two perspectives. First, it improves the robustness of a label posterior-aware graph encoder against false positive links. Second, it identifies missing facts to provide high-quality grounds of reasoning. They are unified in a simple yet effective self-training procedure. Empirically, extensive experiments on three benchmark KG and one Twitter dataset with various degrees of false negative/positive cases demonstrate the effectiveness of nPUGraph.