Co-Certificate Learning with SAT Modulo Symmetries
This addresses a foundational problem in quantum mechanics for researchers in computational logic and graph theory, with incremental improvements over existing SAT-based methods.
The paper tackles the problem of generating all graphs up to isomorphism that satisfy a co-NP property by extending the SAT Modulo Symmetry framework with co-certificate learning, resulting in orders of magnitude faster performance and improved lower bounds for Kochen-Specker vector systems.
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.