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...

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Bibliographic Details
Published inArtificial intelligence Vol. 337; p. 104208
Main Authors Bonacina, Ilario, Bonet, Maria Luisa, Levy, Jordi
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.12.2024
Subjects
Algebraic reasoning
MaxSAT
Polynomial calculus
Proof complexity
Proof systems
SAT
Algebraic reasoning
MaxSAT
Proof systems
68T20
68T15
SAT
03B05
Proof complexity
03F20
03B35
Polynomial calculus
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Summary: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.
ISSN:0004-3702
DOI:10.1016/j.artint.2024.104208