A SAT-based Resolution of Lam's Problem

12/08/2020

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by   Curtis Bright, et al.

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In 1989, computer searches by Lam, Thiel, and Swiercz experimentally resolved Lam's problem from projective geometryx2014the 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 searchesx2014highlighting the difficulty of relying on special-purpose search code for nonexistence results.