Automated SAT Problem Feature Extraction using Convolutional Autoencoders

The Boolean Satisfiability Problem (SAT) was the first known NP-complete problem and has a very broad literature focusing on it. It has been applied successfully to various real-world problems, such as scheduling, planning and cryptography. SAT problem feature extraction plays an essential role in this field. SAT solvers are complex, fine-tuned systems that exploit problem structure. The ability to represent/encode a large SAT problem using a compact set of features has broad practical use in instance classification, algorithm portfolios, and solver configuration. The performance of these techniques relies on the ability of feature extraction to convey helpful information. Researchers often craft these features "by hand" to capture particular structures of the problem. Instead, in this paper, we extract features using semi-supervised deep learning. We train a convolutional autoencoder (AE) to compress the SAT problem into a limited latent space and reconstruct it minimizing the reconstruction error. The latent space projection should preserve much of the structural features of the problem. We compare our approach to a set of features commonly used for algorithm selection. Firstly, we train classifiers on the projection to predict if the problems are satisfiable or not. If the compression conveys valuable information, a classifier should be able to take correct decisions. In the second experiment, we check if the classifiers can identify the original problem that was encoded as SAT. The empirical analysis shows that the autoencoder is able to represent problem features in a limited latent space efficiently, as well as convey more information than current feature extraction methods.