Minimal non-two-colorable hypergraphs and minimal unsatisfiable formulas
Journal of Combinatorial Theory Series A
Investigations on autark assignments
Discrete Applied Mathematics - Special issue on Boolean functions and related problems
Propositional Logic: Deduction and Algorithms
Propositional Logic: Deduction and Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Polynomial-time recognition of minimal unsatisfiable formulas with fixed clause-variable difference
Theoretical Computer Science
A perspective on certain polynomial-time solvable classes of satisfiability
Discrete Applied Mathematics
Lean clause-sets: generalizations of minimally unsatisfiable clause-sets
Discrete Applied Mathematics - The renesse issue on satisfiability
Minimal unsatisfiable formulas with bounded clause-variable difference are fixed-parameter tractable
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
Minimal unsatisfiable formulas with bounded clause-variable difference are fixed-parameter tractable
Journal of Computer and System Sciences
Backdoor Sets of Quantified Boolean Formulas
Journal of Automated Reasoning
Matched formulas and backdoor sets
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
Backdoor sets of quantified boolean formulas
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
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A CNF formula is called matched if its associated bipartite graph (whose vertices are clauses and variables) has a matching that covers all clauses. Matched CNF formulas are satisfiable and can be recognized efficiently by matching algorithms. We generalize this concept and cover clauses by collections of bicliques (complete bipartite graphs). It turns out that such generalization indeed gives rise to larger classes of satisfiable CNF formulas which we term biclique satisfiable. We show, however, that the recognition of biclique satisfiable CNF formulas is NP-complete, and remains NP-hard if the size of bicliques is bounded. A satisfiable CNF formula is called var-satisfiable if it remains satisfiable under arbitrary replacement of literals by their complements. Var-satisfiable CNF formulas can be viewed as the best possible generalization of matched CNF formulas as every matched CNF formula and every biclique satisfiable CNF formula is var-satisfiable. We show that recognition of var-satisfiable CNF formulas is Π2P-complete, answering a question posed by Kleine Büning and Zhao.