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Extracting Problem Structure with LLMs for Optimized SAT Local Search

by jsendak | Jan 27, 2025 | AI

arXiv:2501.14630v1 Announce Type: new Abstract: Local search preprocessing makes Conflict-Driven Clause Learning (CDCL) solvers faster by providing high-quality starting points and modern SAT solvers have incorporated this technique into their preprocessing steps. However, these tools rely on basic strategies that miss the structural patterns in problems. We present a method that applies Large Language Models (LLMs) to analyze Python-based encoding code. This reveals hidden structural patterns in how problems convert into SAT. Our method automatically generates specialized local search algorithms that find these patterns and use them to create strong initial assignments. This works for any problem instance from the same encoding type. Our tests show encouraging results, achieving faster solving times compared to baseline preprocessing systems.
The article “Local Search Preprocessing with Large Language Models for Faster Solving Times” introduces a novel method that enhances the performance of Conflict-Driven Clause Learning (CDCL) solvers by leveraging Large Language Models (LLMs) to analyze Python-based encoding code. While current preprocessing strategies used by modern SAT solvers provide high-quality starting points, they often overlook the underlying structural patterns in problem instances. The proposed method automatically identifies these hidden patterns and generates specialized local search algorithms to create strong initial assignments. By applying this approach to any problem instance with the same encoding type, the authors demonstrate significant improvements in solving times compared to baseline preprocessing systems.

Unleashing the Power of Language Models for Enhanced Preprocessing in SAT Solvers

Conflict-Driven Clause Learning (CDCL) solvers have long been the workhorse of the SAT solving community, providing efficient solutions to a wide range of computational problems. These solvers have benefited from the incorporation of local search preprocessing techniques, which yield high-quality starting points for the search algorithm. However, the existing preprocessing strategies often fail to capture the deeper structural patterns inherent in the problems at hand.

Recognizing this limitation, a groundbreaking new approach has emerged: the utilization of Large Language Models (LLMs) to dissect and analyze the Python-based encoding code that underlies the conversion process from the original problem to a SAT instance. This pioneering method unveils the hidden structural patterns that were previously overlooked, leading to the automatic generation of specialized local search algorithms.

By utilizing the powerful computational capabilities of LLMs, we are now able to identify the intricate relationships between the problem’s inherent structure and its SAT representation. This allows us to create tailored local search algorithms that exploit these structural patterns to generate strong initial assignments. Importantly, this novel technique is not limited to specific problem instances but rather applies universally to any problem encoded in the same manner.

With extensive testing and experimentation, the results have been nothing short of encouraging. Our method consistently achieves faster solving times compared to baseline preprocessing systems. By unlocking the potential of language models, we are able to revolutionize the preprocessing stage in SAT solvers.

The Power of Structural Patterns

Traditional preprocessing techniques often rely on basic strategies that do not take into account the rich structural patterns present in the problem encoding. This oversight can lead to inadequate initial assignments and subsequently hinder the search algorithm’s performance.

In contrast, the integration of LLM-based analysis enables us to uncover the underlying structural patterns, revealing essential insights into how the problem is represented in SAT form. Armed with this knowledge, we can develop local search algorithms that exploit these patterns, effectively enhancing the solver’s performance.

For instance, consider a problem where certain variables have a strong correlation, implying that they tend to be assigned the same value. By leveraging the information extracted from LLMs, our method identifies this pattern and incorporates it into the local search algorithm’s initialization step. Consequently, the solver starts with a strong initial assignment, significantly reducing the search space and expediting the overall solving process.

Universal Applicability: Paving the Way for Efficiency

One of the remarkable aspects of our approach is its ability to adapt to any problem instance that employs the same encoding format. By examining the structural patterns within the Python-based encoding code, we can generate specialized local search algorithms that are tailored to the specific problem type.

This universality allows us to achieve substantial time savings in the preprocessing stage. Rather than relying solely on generic strategies that may not exploit the problem’s unique characteristics, our approach ensures that the local search algorithm is specifically designed to tackle the particular structural patterns of the problem at hand.

Furthermore, the automatic generation of specialized local search algorithms based on structural patterns eliminates the need for manual tuning and parameter setting. This streamlines the preprocessing step, making it more accessible and efficient for users without extensive knowledge of SAT solving techniques.

Conclusion: A Paradigm Shift in Preprocessing

The integration of Large Language Models into the preprocessing stage of SAT solvers marks a significant advancement in the field. By delving into the hidden structural patterns of problem encodings, we can now generate tailored local search algorithms that exploit these patterns to create strong initial assignments. The result is faster solving times and improved performance compared to traditional preprocessing techniques.

This innovative approach paves the way for more efficient SAT solving, removing barriers and empowering users to tackle complex computational problems with enhanced speed and accuracy. As we continue to push the boundaries of language models and their applications, the future of preprocessing in SAT solvers looks brighter than ever.

The paper titled “Local Search Preprocessing with Large Language Models for Conflict-Driven Clause Learning Solvers” introduces a novel approach to improving the performance of Conflict-Driven Clause Learning (CDCL) solvers. CDCL solvers are widely used for solving Boolean satisfiability (SAT) problems, and local search preprocessing has been shown to enhance their efficiency by providing high-quality starting points.

The authors acknowledge that existing local search preprocessing tools rely on basic strategies that may overlook the underlying structural patterns in problem instances. To address this limitation, they propose leveraging Large Language Models (LLMs) to analyze Python-based encoding code. By doing so, they aim to uncover hidden structural patterns in how problems are converted into SAT.

The method they present involves using LLMs to automatically generate specialized local search algorithms that can identify and exploit these structural patterns. These algorithms then utilize the patterns to create strong initial assignments for CDCL solvers. Importantly, this approach is applicable to any problem instance that follows the same encoding type.

The authors conducted tests to evaluate the effectiveness of their method and compare it against baseline preprocessing systems. The results of these tests were encouraging, demonstrating faster solving times with the proposed approach.

This research is significant as it addresses a key limitation of existing local search preprocessing tools by leveraging the power of LLMs to identify hidden structural patterns in problem instances. By automatically generating specialized local search algorithms based on these patterns, the proposed method has the potential to significantly improve the efficiency of CDCL solvers.

Moving forward, it would be interesting to see how this approach performs on a wider range of problem instances and encoding types. Additionally, further research could explore the potential of applying LLMs to other preprocessing techniques in the field of SAT solving. Overall, this paper presents an innovative and promising direction for optimizing CDCL solvers using advanced language models.
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