Identifying Good Rules for Efficient SAT Encodings... | AI Research

Key Takeaways

Identifying Good Rules for Efficient SAT Encodings of Single-Constant Multiplication Using Machine Learning The Single Constant Multiplication (SCM) problem...
The Single Constant Multiplication problem is a fundamental NP-hard optimization task in hardware design, which seeks to decompose a fixed constant using only additions, subtractions, and bit-shifts.
Although dynamic programming methods can produce near-optimal SAT encodings for SCM, their encoding cost remains high for large constants.
We propose a neuro-symbolic framework that accelerates SCM SAT encoding by identifying good rules for guiding operator selection during decomposition.
Our approach employs a graph neural network model to predict promising operator types from constant decompositions, and exploits the resulting confidence scores to prune no-good choices in the symbolic search.

Paper AbstractExpand

The Single Constant Multiplication problem is a fundamental NP-hard optimization task in hardware design, which seeks to decompose a fixed constant using only additions, subtractions, and bit-shifts. Although dynamic programming methods can produce near-optimal SAT encodings for SCM, their encoding cost remains high for large constants. We propose a neuro-symbolic framework that accelerates SCM SAT encoding by identifying good rules for guiding operator selection during decomposition. Our approach employs a graph neural network model to predict promising operator types from constant decompositions, and exploits the resulting confidence scores to prune no-good choices in the symbolic search. Experimental results on unseen 17-32 bit constants demonstrate one to two orders of magnitude reductions in encoding time, over 97% reduction in memory usage, and an order-of-magnitude decrease in branching, while preserving near-optimal encoding quality in terms of additions. These results show that learning-guided symbolic strategies can significantly improve the scalability and efficiency of SCM encoding. Our code and data are publicly available at: this https URL

Identifying Good Rules for Efficient SAT Encodings of Single-Constant Multiplication Using Machine Learning

The Single Constant Multiplication (SCM) problem is a critical challenge in hardware design, involving the decomposition of a constant into simpler operations like additions, subtractions, and bit-shifts. While dynamic programming has traditionally been used to find near-optimal solutions, it becomes computationally expensive when dealing with large constants. This paper introduces a neuro-symbolic framework that combines machine learning with symbolic search to significantly speed up the SAT encoding process for SCM.

The Neuro-Symbolic Approach

The authors propose a method that uses a graph neural network (GNN) to guide the decomposition process. Instead of exploring every possible path to decompose a constant, the GNN predicts which operator types are most promising based on the current state of the decomposition. By assigning confidence scores to these operator choices, the system can effectively "prune" or ignore less efficient paths during the symbolic search. This allows the framework to focus its computational power on the most likely candidates for an optimal solution.

Significant Performance Gains

The experimental results, tested on 17-32 bit constants, show that this learning-guided strategy offers substantial improvements over traditional methods. Key findings include:

Speed: Encoding time is reduced by one to two orders of magnitude.
Memory Efficiency: Memory usage is cut by over 97%.
Search Efficiency: The number of branches required during the search process is reduced by an order of magnitude.
Despite these massive gains in speed and efficiency, the framework successfully maintains near-optimal encoding quality in terms of the number of additions required, proving that the machine learning guidance does not sacrifice the quality of the final hardware design.

Implications for Hardware Design

This research demonstrates that integrating machine learning into symbolic optimization tasks can overcome the scalability limitations of traditional algorithms. By using a GNN to identify "good rules" for operator selection, the authors provide a more efficient path for solving NP-hard optimization tasks in hardware design. The code and data used in this study have been made publicly available to support further research and application in the field.