Polynomial time SAT decision, hypergraph transversals and the hermitian rank

Authors:
Nicola Galesi;Oliver Kullmann
Affiliations:
Departament de Llenguatges i Sistemes Informàtics, Universitat Politécnica de Catalunya, Barcelona, Spain;Computer Science Department, University of Wales Swansea, Swansea, UK
Venue:
SAT'04 Proceedings of the 7th international conference on Theory and Applications of Satisfiability Testing
Year:
2004

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Abstract

Combining graph theory and linear algebra, we study SAT problems of low “linear algebra complexity”, considering formulas with bounded hermitian rank. We show polynomial time SAT decision of the class of formulas with hermitian rank at most one, applying methods from hypergraph transversal theory. Applications to heuristics for SAT algorithms and to the structure of minimally unsatisfiable clause-sets are discussed.