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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.