Generating non-analytic cuts for boolean formulas with linear programming

• Ano de defesa: 2026
• Autor(a) principal: Pevidor, João Felipe Lobo
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Approximation of logical systems; Aproximação de sistemas lógicos; Boolean satisfiability; Integer programming; Linear programming; Optimization; Otimização; Programação inteira; Programação linear; Satisfabilidade booleana
• Link de acesso: https://teses.usp.br/teses/disponiveis/45/45134/tde-01042026-180812/

The Boolean satisfiability problem is the most notorious and first ever discovered NP-Complete problem. To solve it, state-of-the-art methods still rely on techniques that yield exponential running time in the worst case. The goal of this work is to study methods used on correlated problems in order to approach solving a SAT instance from a different angle, that can be seen as the generation of non-analytic cuts supported by a linear algebra. In particular, linear programming methods have obtained good results when dealing with a closely related problem, the satisfiability problem in infinitely valued logics. With that in mind, we will study the original SAT as an optimization problem. We present a new way of generating non-analytic cuts for a boolean formula by solving a linear programming problem. From the linear solution, boolean values are extracted, and a partial solution is constructed and evolved until a conflict is detected. Using the conflict, we implement clausal learning to produce a new clause. We also present a complete SAT solving algorithm designed to leverage this method, show soundness and completeness results for it and investigate its empirical performance.