An explicit semidefinite characterization of satisfiability for Tseitin instances on toroidal grid graphs

Authors:
Miguel F. Anjos
Affiliations:
Department of Management Sciences, University of Waterloo, Waterloo, Canada N2L 3G1
Venue:
Annals of Mathematics and Artificial Intelligence
Year:
2006

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Abstract

This paper is concerned with the application of semidefinite programming to the satisfiability problem, and in particular with using semidefinite liftings to efficiently obtain proofs of unsatisfiability. We focus on the Tseitin satisfiability instances which are known to be hard for many proof systems. For Tseitin instances based on toroidal grid graphs, we present an explicit semidefinite programming problem with dimension linear in the size of the Tseitin instance, and prove that it characterizes the satisfiability of these instances, thus providing an explicit certificate of satisfiability or unsatisfiability.