The paper Finding Periodic Apartments via Boolean Satisfiability and Orderly Generation by Jarkko Savela, Emilia Oikarinen, and Matti Järvisalo has been accepted for publication in the proceedings of the 23rd International Conference on Logic for Programming, Artificial Intelligence and Reasoning (LPAR-23).
Motivated by Gromov’s subgroup conjecture (GSC), a fundamental open conjecture in the area of geometric group theory, the work tackles the problem of the existence of partic- ular types of subgroups—arising from so-called periodic apartments—for a specific set of hyperbolic groups with respect to which GSC is currently open. This problem is equivalent to determining whether specific types of graphs with a non-trivial combination of properties exist. The existence of periodic apartments allows for ruling the groups out as some of the remaining potential counterexamples to GSC. The paper developed an approach that combines both automated reasoning techniques—in particular, Boolean satisfiability (SAT) solving—with problem-specific orderly generation. Compared to earlier attempts to tackle the problem through computational means, the approach scales noticeably better, and allows for both confirming results from a previous computational treatment for smaller parameter values as well as ruling out further groups out as potential counterexamples to GSC.