G2SAT: Learning to Generate SAT Formulas

TL;DR

G2SAT is a deep generative framework that learns to produce realistic SAT formulas from input data, aiding in solver development and understanding by creating synthetic benchmarks that resemble real-world instances.

Contribution

This work introduces G2SAT, the first neural network-based method to generate SAT formulas that mimic real-world instances using graph representations.

Findings

G2SAT generates SAT formulas closely resembling real-world instances.

Synthetic formulas improve SAT solver performance on benchmarks.

The approach captures characteristics of real SAT formulas through graph metrics.

Abstract

The Boolean Satisfiability (SAT) problem is the canonical NP-complete problem and is fundamental to computer science, with a wide array of applications in planning, verification, and theorem proving. Developing and evaluating practical SAT solvers relies on extensive empirical testing on a set of real-world benchmark formulas. However, the availability of such real-world SAT formulas is limited. While these benchmark formulas can be augmented with synthetically generated ones, existing approaches for doing so are heavily hand-crafted and fail to simultaneously capture a wide range of characteristics exhibited by real-world SAT instances. In this work, we present G2SAT, the first deep generative framework that learns to generate SAT formulas from a given set of input formulas. Our key insight is that SAT formulas can be transformed into latent bipartite graph representations which we model using a specialized deep generative neural network. We show that G2SAT can generate SAT formulas that closely resemble given real-world SAT instances, as measured by both graph metrics and SAT solver behavior. Further, we show that our synthetic SAT formulas could be used to improve SAT solver performance on real-world benchmarks, which opens up new opportunities for the continued development of SAT solvers and a deeper understanding of their performance.