Matrix analysis
On the complexity of cutting-plane proofs
Discrete Applied Mathematics
A hierarchy of relaxation between the continuous and convex hull representations
SIAM Journal on Discrete Mathematics
SIAM Review
Elliptic approximations of propositional formulae
Discrete Applied Mathematics - Special issue on the satisfiability problem and Boolean functions
Recognition of tractable satisfiability problems through balanced polynomial representations
Proceedings of the 5th Twente workshop on on Graphs and combinatorial optimization
A machine program for theorem-proving
Communications of the ACM
A 7/8-Approximation Algorithm for MAX 3SAT?
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Gadgets Approximation, and Linear Programming
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Approximating the value of two power proof systems, with applications to MAX 2SAT and MAX DICUT
ISTCS '95 Proceedings of the 3rd Israel Symposium on the Theory of Computing Systems (ISTCS'95)
Solving Satisfiability Problems Using Elliptic Approximations. A Note on Volumes and Weights
Annals of Mathematics and Artificial Intelligence
On Semidefinite Programming Relaxations of (2+p)-SAT
Annals of Mathematics and Artificial Intelligence
Annals of Mathematics and Artificial Intelligence
A new incomplete method for CSP inconsistency checking
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
Generalising Unit-Refutation Completeness and SLUR via Nested Input Resolution
Journal of Automated Reasoning
Semidefinite resolution and exactness of semidefinite relaxations for satisfiability
Discrete Applied Mathematics
Hi-index | 0.00 |
We derive a semidefinite relaxation of the satisfiability (SAT) problem and discuss its strength. We give both the primal and dual formulation of the relaxation. The primal formulation is an eigenvalue optimization problem, while the dual formulation is a semidefinite feasibility problem. We show that using the relaxation, a proof of the unsatisfiability of the notorious pigeonhole and mutilated chessboard problems can be computed in polynomial time. As a byproduct we find a new `sandwich" theorem that is similar to the sandwich theorem for Lovász' ϑ-function. Furthermore, the semidefinite relaxation gives a certificate of (un)satisfiability for 2SAT problems in polynomial time. By adding an objective function to the dual formulation, a specific class of polynomially solvable 3SAT instances can be identified. We conclude with discussing how the relaxation can be used to solve more general SAT problems and with some empirical observations.