# A Solver-in-the-Loop Framework for Improving LLMs on Answer Set Programming for Logic Puzzle Solving

arXiv: https://arxiv.org/abs/2512.17093 · HTML: https://mlsanity.com/paper/2512.17093/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 36 references that are in the map.
- First posted on arXiv 18 Dec 2025.

## Builds on (most cited first, 15 of 15)

- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [A Survey on Large Language Models for Code Generation](https://mlsanity.com/paper/2406.00515/) (2024)
- [Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning](https://mlsanity.com/paper/2305.12295/) (2023)
- [Step-DPO: Step-wise Preference Optimization for Long-chain Reasoning of LLMs](https://mlsanity.com/paper/2406.18629/) (2024)
- [NeuroLogic A*esque Decoding: Constrained Text Generation with Lookahead Heuristics](https://mlsanity.com/paper/2112.08726/) (2021)
- [Multi-shot ASP solving with clingo](https://mlsanity.com/paper/1705.09811/) (2017)
- [SteerLM: Attribute Conditioned SFT as an (User-Steerable) Alternative to RLHF](https://mlsanity.com/paper/2310.05344/) (2023)
- [Skeleton-of-Thought: Prompting LLMs for Efficient Parallel Generation](https://mlsanity.com/paper/2307.15337/) (2023)
- [A Comprehensive Survey of Direct Preference Optimization: Datasets, Theories, Variants, and Applications](https://mlsanity.com/paper/2410.15595/) (2024)
- [Step-by-Step Reasoning to Solve Grid Puzzles: Where do LLMs Falter?](https://mlsanity.com/paper/2407.14790/) (2024)
- [Arithmetic Reasoning with LLM: Prolog Generation & Permutation](https://mlsanity.com/paper/2405.17893/) (2024)
- [A Survey on LLM Inference-Time Self-Improvement](https://mlsanity.com/paper/2412.14352/) (2024)
- [QUITE: Quantifying Uncertainty in Natural Language Text in Bayesian Reasoning Scenarios](https://mlsanity.com/paper/2410.10449/) (2024)
- [From An LLM Swarm To A PDDL-Empowered HIVE: Planning Self-Executed Instructions In A Multi-Modal Jungle](https://mlsanity.com/paper/2412.12839/) (2024)

## Built on by (most cited first, 4 of 4)

- [Pencil Puzzle Bench: A Benchmark for Multi-Step Verifiable Reasoning](https://mlsanity.com/paper/2603.02119/) (2026)
- [Modeling Next-Token Prediction as Left-Nested Intuitionistic Implication](https://mlsanity.com/paper/2601.19915/) (2026)
- [BLAST: Benchmarking LLMs with ASP-based Structured Testing](https://mlsanity.com/paper/2604.22306/) (2026)
- [Distilling Answer Set Programming Theories from Large Language Models](https://mlsanity.com/paper/2607.28086/) (2026)

## Abstract (arXiv)

The rise of large language models (LLMs) has sparked interest in coding assistants. While general-purpose programming languages are well supported, generating code for domain-specific languages remains a challenging problem for LLMs. In this paper, we focus on the LLM-based generation of code for Answer Set Programming (ASP), a particularly effective approach for finding solutions to combinatorial search problems. The effectiveness of LLMs in ASP code generation is currently hindered by the limited number of examples seen during their initial pre-training phase. In this paper, we introduce a novel ASP-solver-in-the-loop approach for solver-guided instruction-tuning of LLMs to addressing the highly complex semantic parsing task inherent in ASP code generation. Our method only requires problem specifications in natural language and their solutions. Specifically, we sample ASP statements for program continuations from LLMs for unriddling logic puzzles. Leveraging the special property of declarative ASP programming that partial encodings increasingly narrow down the solution space, we categorize them into chosen and rejected instances based on solver feedback. We then apply supervised fine-tuning to train LLMs on the curated data and further improve robustness using a solver-guided search that includes best-of-N sampling. Our experiments demonstrate consistent improvements in two distinct prompting settings on two datasets.