Co-Certificate Learning with SAT Modulo Symmetries

TL;DR

This paper introduces a novel SAT-based approach called co-certificate learning within the SMS framework to efficiently generate all graphs up to isomorphism satisfying a co-NP property, significantly advancing quantum mechanics research.

Contribution

It extends the SMS framework with co-certificate learning, enabling faster and more scalable generation of graphs meeting co-NP properties, improving bounds on Kochen-Specker vector systems.

Findings

Orders of magnitude faster than previous methods

Significantly better scalability

Improved lower bounds on Kochen-Specker vector systems

Abstract

We present a new SAT-based method for generating all graphs up to isomorphism that satisfy a given co-NP property. Our method extends the SAT Modulo Symmetry (SMS) framework with a technique that we call co-certificate learning. If SMS generates a candidate graph that violates the given co-NP property, we obtain a certificate for this violation, i.e., `co-certificate' for the co-NP property. The co-certificate gives rise to a clause that the SAT solver, serving as SMS's backend, learns as part of its CDCL procedure. We demonstrate that SMS plus co-certificate learning is a powerful method that allows us to improve the best-known lower bound on the size of Kochen-Specker vector systems, a problem that is central to the foundations of quantum mechanics and has been studied for over half a century. Our approach is orders of magnitude faster and scales significantly better than a recently proposed SAT-based method.