Linear CNF formulas and satisfiability

Linear CNF formulas and satisfiability

In this paper, we study linear CNF formulas generalizing linear hypergraphs un-der combinatorial and complexity theoretical aspects w.r.t. SAT. We establish NP-completeness of SAT for the unrestricted linear formula class, and we show the equiv-alence of NP-completeness of restricted uniform linear formula classes w.r.t. SATand the existence of unsatisfiable uniform linear witne...

Satisfiability of Almost Disjoint CNF Formulas

We call a CNF formula linear if any two clauses have at most one variable in common. Let m(k) be the largest integer m such that any linear k-CNF formula with ≤ m clauses is satisfiable. We show that 4 k 4e2k3 ≤ m(k) < ln(2)k4. More generally, a (k, d)-CSP is a constraint satisfaction problem in conjunctive normal form where each variable can take on one of d values, and each constraint contain...

Satisfiability of Acyclic and almost Acyclic CNF Formulas (II)

We show that the SATISFIABILITY (SAT) problem for CNF formulas with β-acyclic hypergraphs can be solved in polynomial time by using a special type of Davis-Putnam resolution where each resolvent is a subset of a parent clause. We extend this class to CNF formulas for which this type of Davis-Putnam resolution still applies and show that testing membership in this class is NP-complete. We compar...

Satisfiability of Acyclic and Almost Acyclic CNF Formulas

We show that the SATISFIABILITY (SAT) problem for CNF formulas with β-acyclic hypergraphs can be solved in polynomial time by using a special type of Davis-Putnam resolution where each resolvent is a subset of a parent clause. We extend this class to CNF formulas for which this type of DavisPutnam resolution still applies and show that testing membership in this class is NP-complete. We compare...

A CNF Class Generalizing Exact Linear Formulas