A SAT-based Resolution of Lam's Problem


  • Curtis Bright University of Windsor Carleton University
  • Kevin K. H. Cheung Carleton University
  • Brett Stevens Carleton University
  • Ilias Kotsireas Wilfrid Laurier University
  • Vijay Ganesh University of Waterloo


Satisfiability, Search, Applications


In 1989, computer searches by Lam, Thiel, and Swiercz experimentally resolved Lam's problem from projective geometry—the long-standing problem of determining if a projective plane of order ten exists. Both the original search and an independent verification in 2011 discovered no such projective plane. However, these searches were each performed using highly specialized custom-written code and did not produce nonexistence certificates. In this paper, we resolve Lam's problem by translating the problem into Boolean logic and use satisfiability (SAT) solvers to produce nonexistence certificates that can be verified by a third party. Our work uncovered consistency issues in both previous searches—highlighting the difficulty of relying on special-purpose search code for nonexistence results.




How to Cite

Bright, C., Cheung, K. K. H., Stevens, B., Kotsireas, I., & Ganesh, V. (2021). A SAT-based Resolution of Lam’s Problem. Proceedings of the AAAI Conference on Artificial Intelligence, 35(5), 3669-3676. Retrieved from https://ojs.aaai.org/index.php/AAAI/article/view/16483



AAAI Technical Track on Constraint Satisfaction and Optimization