Abstract
The evolution of Large Language Models (LLMs) from static instruction-followers to autonomous agents necessitates operating within complex, stateful environments to achieve precise state-transition objectives. However, this paradigm is bottlenecked by data scarcity, as existing tool-centric reverse-synthesis pipelines fail to capture the rigorous logic of real-world applications. We introduce \textbf\{LOGIGEN\}, a logic-driven framework that synthesizes verifiable training data based on three core pillars: \textbf\{Hard-Compiled Policy Grounding\}, \textbf\{Logic-Driven Forward Synthesis\}, and \textbf\{Deterministic State Verification\}. Specifically, a Triple-Agent Orchestration is employed: the \textbf\{Architect\} compiles natural-language policy into database constraints to enforce hard rules; the \textbf\{Set Designer\} initializes boundary-adjacent states to trigger critical policy conflicts; and the \textbf\{Explorer\} searches this environment to discover causal solution paths