Structure based SAT dataset for analysing GNN generalisation

TL;DR

This paper introduces StructureSAT, a curated dataset of SAT problems with diverse structural properties, to analyze and improve the generalization of GNN-based SAT solvers by leveraging graph-theoretic measures.

Contribution

It presents a novel dataset and splitting method that focus on structural properties of SAT problems to study GNN generalization issues.

Findings

Dataset enables analysis of structural influences on GNN performance.

Structural properties correlate with GNN generalization ability.

Future directions for developing more robust GNN SAT solvers.

Abstract

Satisfiability (SAT) solvers based on techniques such as conflict driven clause learning (CDCL) have produced excellent performance on both synthetic and real world industrial problems. While these CDCL solvers only operate on a per-problem basis, graph neural network (GNN) based solvers bring new benefits to the field by allowing practitioners to exploit knowledge gained from solved problems to expedite solving of new SAT problems. However, one specific area that is often studied in the context of CDCL solvers, but largely overlooked in GNN solvers, is the relationship between graph theoretic measure of structure in SAT problems and the generalisation ability of GNN solvers. To bridge the gap between structural graph properties (e.g., modularity, self-similarity) and the generalisability (or lack thereof) of GNN based SAT solvers, we present StructureSAT: a curated dataset, along with code to further generate novel examples, containing a diverse set of SAT problems from well known problem domains. Furthermore, we utilise a novel splitting method that focuses on deconstructing the families into more detailed hierarchies based on their structural properties. With the new dataset, we aim to help explain problematic generalisation in existing GNN SAT solvers by exploiting knowledge of structural graph properties. We conclude with multiple future directions that can help researchers in GNN based SAT solving develop more effective and generalisable SAT solvers.