Journal of the ACM (JACM)
Some results and experiments in programming techniques for propositional logic
Computers and Operations Research - Special issue: Applications of integer programming
On Semidefinite Programming Relaxations of (2+p)-SAT
Annals of Mathematics and Artificial Intelligence
An Explicit Equivalent Positive Semidefinite Program for Nonlinear 0-1 Programs
SIAM Journal on Optimization
Relaxations of the Satisfiability Problem Using Semidefinite Programming
Journal of Automated Reasoning
An improved semidefinite programming relaxation for the satisfiability problem
Mathematical Programming: Series A and B
Annals of Mathematics and Artificial Intelligence
Sums of squares based approximation algorithms for MAX-SAT
Discrete Applied Mathematics
Sums of squares, satisfiability and maximum satisfiability
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
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This paper explores new connections between the satisfiability problem and semidefinite programming. We show how the process of resolution in satisfiability is equivalent to a linear transformation between the feasible sets of the relevant semidefinite programming problems. We call this transformation semidefinite programming resolution, and we demonstrate the potential of this novel concept by using it to obtain a direct proof of the exactness of the semidefinite formulation of satisfiability without applying Lasserre's general theory for semidefinite relaxations of 0/1 problems. In particular, our proof explicitly shows how the exactness of the semidefinite formulation for any satisfiability formula can be interpreted as the implicit application of a finite sequence of resolution steps to verify whether the empty clause can be derived from the given formula.