Generalizations of matched CNF formulas

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...

The Sat Problem of Signed Cnf Formulas

Signed conjunctive normal form (signed CNF) is a classical conjunctive clause form using a generalised notion of literal, called signed literal. A signed literal is an expression of the form S : p, where p is a classical atom and S, its sign, is a subset of a domain N . The informal meaning is “p takes one of the values in S”. Signed formulas are a logical language for knowledge representation ...

Clause Elimination Procedures for CNF Formulas

Abstract. We develop and analyze clause elimination procedures, a specific family of simplification techniques for conjunctive normal form (CNF) formulas. Extending known procedures such as tautology, subsumption, and blocked clause elimination, we introduce novel elimination procedures based on hidden and asymmetric variants of these techniques. We analyze the resulting nine (including five ne...

Resolution Methods for Many - Valued CNF Formulas