A Category-Theoretic Approach to Neural-Symbolic Task Planning with Bidirectional Search

We introduce a Neural-Symbolic Task Planning framework integrating Large Language Model (LLM) decomposition with categorytheoretic verification for resource-aware, temporally consistent planning. Our approach represents states as objects and valid operations as morphisms in a categorical framework, ensuring constraint satisfaction through mathematical pullbacks. We employ bidirectional search that simultaneously expands from initial and goal states, guided by a learned planning distance function that efficiently prunes infeasible paths. Empirical evaluations across three planning domains demonstrate that our method improves completion rates by up to 6.6% and action accuracy by 9.1%, while eliminating resource violations compared to the existing baselines. These results highlight the synergy between LLM-based operator generation and category-theoretic verification for reliable planning in domains requiring both resourceawareness and temporal consistency.