Polynomial calculus for optimization
MaxSAT is the problem of finding an assignment satisfying the maximum number of clauses in a CNF formula. We consider a natural generalization of this problem to generic sets of polynomials and propose a weighted version of Polynomial Calculus to address this problem. Weighted Polynomial Calculus is...
| Autores: | , , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/416840 |
| Acceso en línea: | https://hdl.handle.net/2117/416840 https://dx.doi.org/10.1016/j.artint.2024.104208 |
| Access Level: | acceso abierto |
| Palabra clave: | MaxSAT SAT Proof systems Polynomial calculus Algebraic reasoning Proof complexity Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de cossos i polinomis |
| Sumario: | MaxSAT is the problem of finding an assignment satisfying the maximum number of clauses in a CNF formula. We consider a natural generalization of this problem to generic sets of polynomials and propose a weighted version of Polynomial Calculus to address this problem. Weighted Polynomial Calculus is a natural generalization of the systems MaxSAT-Resolution and weighted Resolution. Unlike such systems, weighted Polynomial Calculus manipulates polynomials with coefficients in a finite field and either weights in ℕ or ℤ. We show the soundness and completeness of weighted Polynomial Calculus via an algorithmic procedure. Weighted Polynomial Calculus, with weights in ℕ and coefficients in F2, is able to prove efficiently that Tseitin formulas on a connected graph are minimally unsatisfiable. Using weights in ℤ, it also proves efficiently that the Pigeonhole Principle is minimally unsatisfiable. |
|---|