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

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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.

Keywords

satisfiability problem semidefinite programming combinatorial optimization discrete optimization global optimization 

Mathematics Subject Classifications (2000)

90C22 68T15 03B05 90C90 90C09 

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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  1. 1.Department of Management SciencesUniversity of WaterlooWaterlooCanada

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