Satisfiability of Acyclic and Almost Acyclic CNF Formulas

Sebastian Ordyniak, Daniel Paulusma & Stefan Szeider
We study the propositional satisfiability problem (SAT) on classes of CNF formulas (formulas in Conjunctive Normal Form) that obey certain structural restrictions in terms of their hypergraph structure, by associating to a CNF formula the hypergraph obtained by ignoring negations and considering clauses as hyperedges on variables. We show that satisfiability of CNF formulas with so-called ``beta-acyclic hypergraphs'' can be decided in polynomial time. We also study the parameterized complexity of SAT for ``almost'' beta-acyclic...