## 3 Related Work  
Traditionally, CP and LLMs have developed independently of each other, with little collaboration. Recent advances in LLMs present opportunities to integrate these fields. Two approaches are emerging: using CP to improve LLM capabilities, and leveraging LLMs to enhance CP. Several studies [4; 5] have explored the first approach. The authors of [4] explored why LLMs sometimes generate factually incorrect information. The authors found that by analyzing the attention patterns of large language models, they could predict when the model might make a factual error. They call this method SAT Probe, and it essentially looks at how much attention LLMs pay to specific constraints within a given prompt. The more attention paid to these constraints, the more likely the LLM is to generate factually accurate text. The authors of [5] discussed how to combine constraint programming with large language models for improved text generation. The authors argued that while constraint programming excels at handling structural constraints, it struggles with incorporating \"meaning\", which LLMs are adept at. The study introduced GenCP, an approach that integrates an LLM into a CP solver. This allows the LLM to generate text while the CP framework ensures all constraints are met. The authors also demonstrated that GenCP outperforms traditional Natural Language Processing (NLP) methods such as Beam Search, producing higher-quality results more efficiently. Essentially, their study proposes a synergistic approach where LLMs and CP work together to overcome their individual limitations, opening up new possibilities for text generation under constraints. Our study focuses on the second approach, using large language models to enhance constraint programming. Several studies have explored using large language models (LLMs) for constraint programming (CP) code generation, including the generation of constraint models [17; 18; 19]. All of these studies recognized the complexity of the constraint model generated, and the most successful ones split the problem into two parts: the recognition of optimization problem entities, called Named Entity Recognition (NER), and generation of problem formulation. Building on this research, a study [17] proposed a generative model capable of automatically generating CP models from natural language descriptions. It uses an NER method similar to [18] to extract semantic entities. Then, it uses retrieval-augmented generation (RAG) [33] with in-context learning (ICL) [32] to create a blueprint model with extracted semantic entities. RAG uses embedding to find semantically similar predefined models, and those retrieved semantically similar natural language descriptions are used as ICL examples when prompting an LLM to generate a formal model. While the potential of using large language models for code generation has been explored [8; 34], there is a lack of research on their use to generate complex constraint satisfaction models. Existing work has focused on exploring the ability of LLMs to generate a simple optimization model [16]. This study uses a vanilla method to generate basic constrained optimization (COP) models with the necessary constraints and variables. The vanilla method only generated elementary models, or both constraint satisfaction and optimization models. The authors of [16] did not define a specific problem description in natural language but, rather, a natural language task that prompts an LLM to generate an arbitrary model in order to explore the ability of LLMs to generate rudimentary COP and CSP models. Our study defines specific, not arbitrary, configuration tasks in natural language. Constraint satisfaction problems are well suited to defining the closed space of a configuration [1; 17]. Our study defines specific tasks in natural language and asks LLMs to solve them.