A Reality Check of Language Models as Formalizers on Constraint Satisfaction Problems

Recent work shows superior performance when using large language models (LLMs) as formalizers instead of as end-to-end solvers for symbolic reasoning problems. Given the problem description, the LLM generates a formal program that derives a solution via an external solver. We systematically investigate the formalization capability of LLMs on real-life constraint satisfaction problems on 4 benchmarks, 6 LLMs, and 2 types of formal languages. We show that LLM-as-formalizer by no means trivializes the problem but underperforms LLM-as-solver in 15 out of 24 model-dataset combinations, despite the former's verifiability and interpretability. Although the formalization space is magnitudes smaller than the search space, our scaling analysis shows that LLM-as-formalizer still drastically degrades as problem complexity increases similar to LLM-as-solver. To better understand this limitation, we observe excessive, solver-like reasoning tokens that sometimes lead to hard-coded solutions, highlighting a key challenge for improving LLM-based formalization.