اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدA SAT-based Resolution of Lams Problem
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In 1989, computer searches by Lam, Thiel, and Swiercz experimentally resolved Lams problem from projective geometry$unicode{x2014}$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 Lams 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$unicode{x2014}$highlighting the difficulty of relying on special-purpose search code for nonexistence results.
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