Work

Polynomial calculus for optimization

Year: 2024

Type: article

Abstract: 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.

Source: Artificial Intelligence

DOI: 10.1016/j.artint.2024.104208

Authors: Ilario Bonacina, Maria Luisa Bonet, Jordi Levy

Institutions: Universitat Politècnica de Catalunya, Consejo Superior de Investigaciones Científicas, Artificial Intelligence Research Institute

Language: English

Topic: Constraint Satisfaction and Optimization

Subfield: Computer Networks and Communications

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,070

Funders: Simons Institute for the Theory of Computing, University of California Berkeley, Agencia Estatal de Investigación