# CP-SynC: Multi-Agent Zero-Shot Constraint Modeling in MiniZinc with Synthesized Checkers

arXiv: https://arxiv.org/abs/2605.01675 · HTML: https://mlsanity.com/paper/2605.01675/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in General LLM agent frameworks and benchmarks, one of 16 directions in LLM agents and tool use.
- Builds on 14 of its 28 references that are in the map.
- First posted on arXiv 3 May 2026.

## Placed in

- LLM agents and tool use / [General LLM agent frameworks and benchmarks](https://mlsanity.com/agents/general-llm-agent-frameworks-and-benchmarks/)

## Builds on (most cited first, 14 of 14)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [Teaching Large Language Models to Self-Debug](https://mlsanity.com/paper/2304.05128/) (2023)
- [Large Language Models as End-to-end Combinatorial Optimization Solvers](https://mlsanity.com/paper/2509.16865/) (2025)
- [Revisit Self-Debugging with Self-Generated Tests for Code Generation](https://mlsanity.com/paper/2501.12793/) (2025)
- [Generating Streamlining Constraints with Large Language Models](https://mlsanity.com/paper/2408.10268/) (2024)
- [Pragmatic Reasoning improves LLM Code Generation](https://mlsanity.com/paper/2502.15835/) (2025)
- [Text2Zinc: A Cross-Domain Dataset for Modeling Optimization and Satisfaction Problems in MiniZinc](https://mlsanity.com/paper/2503.10642/) (2025)
- [Operational Research: Methods and Applications](https://mlsanity.com/paper/2303.14217/) (2023)
- [CP-Agent: Agentic Constraint Programming](https://mlsanity.com/paper/2508.07468/) (2025)
- [Variational Prefix Tuning for Diverse and Accurate Code Summarization Using Pre-trained Language Models](https://mlsanity.com/paper/2505.09062/) (2025)

## Built on by (most cited first, 2 of 2)

- [Formalize, Don't Optimize: The Heuristic Trap in LLM-Generated Combinatorial Solvers](https://mlsanity.com/paper/2605.12421/) (2026)
- [OR for AI That Does OR: Routing LLMs up the Escalator inside the OSCAR Framework](https://mlsanity.com/paper/2610.00912/) (2026)

## Abstract (arXiv)

Constraint Programming (CP) is a powerful paradigm for solving combinatorial problems, yet translating natural language problem descriptions into executable models remains a significant bottleneck. While Large Language Models (LLMs) show promise in automating this translation, they often struggle with subtle semantic errors in the absence of oracle validation at test time. To address this, we introduce CP-SynC (Constraint Programming modeling with Synthesized Checkers), a multi-agent workflow for zero-shot constraint modeling in MiniZinc. CP-SynC coordinates modeling agents that generate and refine candidate models and validation agents that synthesize semantic checkers to provide feedback on semantic correctness. To mitigate noise inherent in individual LLM outputs, CP-SynC explores multiple modeling trajectories in parallel and employs selection agents to select the final model via multi-agent evidence aggregation. Extensive experiments on a benchmark of 100 CP problems show that CP-SynC substantially outperforms existing baselines in MiniZinc modeling.