A SAT-based Resolution of Lam's Problem (SAT instances and certificates)

This repository contains SAT instances and certificates accompanying the paper "A SAT-based Resolution of Lam's Problem" appearing at AAAI 2021.  This paper developed a method to generate certificates proving the nonexistence of a word of weight 19 in the code generated by a projective plane of order ten.  Together with previously computed certificates this solves Lam's Problem.

The 'a1' archive contains a certificate showing that there are exactly 66 A1 matrices up to isomorphism.  Run the provided check.sh script to verify the certificate.

The 'a2' archive contains certificates showing that there are exactly 650,370 A2 matrices up to isomorphism.  Run the provided check.sh script to verify the certificates.

The 'main' archive contains precomputed SAT instances for each of the A2 matrices up to isomorphism and partial solutions of the SAT instances.  The main certificates may be generated and verified by extracting the main archive into the weight19/main directory of the MathCheck2 repository for Lam's problem (available from bitbucket.org/cbright/mathcheck2) and running the driver.sh script.  The final-step/solve.sh script verifies that no partial solution can be completed to a full incidence matrix of a projective plane of order ten.