When Planning Problems Become Hard for LLMs: Separating Structural Complexity from Semantic Interpretability

Overview & Synopsis

Large language models (LLMs) struggle with classical planning, but benchmarks rarely distinguish structural difficulty from the difficulty of interpreting symbolic vocabulary. We examine seven STRIPS domains with BFS-optimal plan lengths. For predicting structural difficulty without solving an instance, the zero-training delete-relaxation heuristic $h_{\mathrm{add}}$ outperforms learned alternatives on held-out domains (mean Spearman $|ρ|=0.931$), including ridge regression ($0.707$), object count ($0.657$), and the episodic retrieval architecture ARC ($0.400$). ARC also fails to outperform a linear model using the same features. To isolate semantic effects, we progressively rename predicates while preserving states, transitions, and optimal plans. Valid LLM planning success drops from $67.5\%$ to $40.0\%$ between $0\%$ and $100\%$ renaming, while refusals remain at $0\%$. An LLM supplied with ARC's conditioning information predicts difficulty in context better than trained ARC (mean $|ρ|=0.826$). Hybrid routing between an LLM and a symbolic planner depends more on calibration to the target LLM's outcomes than on the structural score selected. Thus, established symbolic heuristics already estimate structural difficulty well; improving hybrid planning requires modeling LLM behavior sensitive to predicate semantics rather than developing more structural predictors.