HardSATGEN: Understanding the Difficulty of Hard SAT Formula Generation and A Strong Structure-Hardness-Aware Baseline

TL;DR

HardSATGEN is a novel SAT formula generation method that better captures industrial formula structures and hardness, significantly improving the quality of generated instances for solver tuning.

Contribution

We introduce HardSATGEN, a fine-grained control mechanism for neural split-merge in SAT generation, addressing previous limitations in reproducing hardness and structural properties.

Findings

HardSATGEN outperforms previous methods in structural similarity and hardness preservation.

Generated instances significantly improve solver tuning effectiveness.

Experiments on private and corporate benchmarks validate the approach.

Abstract

Industrial SAT formula generation is a critical yet challenging task. Existing SAT generation approaches can hardly simultaneously capture the global structural properties and maintain plausible computational hardness. We first present an in-depth analysis for the limitation of previous learning methods in reproducing the computational hardness of original instances, which may stem from the inherent homogeneity in their adopted split-merge procedure. On top of the observations that industrial formulae exhibit clear community structure and oversplit substructures lead to the difficulty in semantic formation of logical structures, we propose HardSATGEN, which introduces a fine-grained control mechanism to the neural split-merge paradigm for SAT formula generation to better recover the structural and computational properties of the industrial benchmarks. Experiments including evaluations on private and practical corporate testbed show the superiority of HardSATGEN being the only method to successfully augment formulae maintaining similar computational hardness and capturing the global structural properties simultaneously. Compared to the best previous methods, the average performance gains achieve 38.5% in structural statistics, 88.4% in computational metrics, and over 140.7% in the effectiveness of guiding solver tuning by our generated instances. Source code is available at http://github.com/Thinklab-SJTU/HardSATGEN