Year: 2008
Type: preprint
Abstract: A pair of clauses in a CNF formula constitutes a conflict if there is a variable that occurs positively in one clause and negatively in the other. A CNF formula without any conflicts is satisfiable. The Lovasz Local Lemma implies that a k-CNF formula is satisfiable if each clause conflicts with at most 2^k/e-1 clauses. It does not, however, give any good bound on how many conflicts an unsatisfiable formula has globally. We show here that every unsatisfiable k-CNF formula requires 2.69^k conflicts and there exist unsatisfiable k-CNF formulas with 3.51^k conflicts.
Source: arXiv (Cornell University)
Authors: Scheder, Dominik, Zumstein, Philipp
Language: English
Subfield: Computer Networks and Communications
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1644819540