Guiding SAT Diagnosis with Tree Decompositions

The topological structure of a CNF formula can be represented as a hypergraph, where the vertices of the hypergraph correspond to the variables of the CNF and the hyperedges correspond to the clauses. Given a small treewidth tree decomposition for a hypergraph of a CNF formula, a variety of methods are known for deciding its satisfiability. In this paper we report on our effort to learn whether the theoretical applicability of tree decomposition to SAT can be made to work in practice. To do this, we attempt to find tree decompositions of small treewidth for significant problems, and to incorporate methods based on tree decomposition into a state-of-the-art SAT solver.