Minimal non-two-colorable hypergraphs and minimal unsatisfiable formulas
Journal of Combinatorial Theory Series A
Directed hypergraphs and applications
Discrete Applied Mathematics - Special issue: combinatorial structures and algorithms
Which problems have strongly exponential complexity?
Journal of Computer and System Sciences
Tuning SAT Checkers for Bounded Model Checking
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
An Application of Matroid Theory to the SAT Problem
COCO '00 Proceedings of the 15th Annual IEEE Conference on Computational Complexity
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
On finding short resolution refutations and small unsatisfiable subsets
Theoretical Computer Science - Parameterized and exact computation
On the parameterized complexity of multiple-interval graph problems
Theoretical Computer Science
Backbones and backdoors in satisfiability
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 3
Journal of Artificial Intelligence Research
A backbone-search heuristic for efficient solving of hard 3-SAT formulae
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Backbones in optimization and approximation
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Minimum 2CNF resolution refutations in polynomial time
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
Pushing the envelope: planning, propositional logic, and stochastic search
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 2
Clustering at the phase transition
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
Minimum witnesses for unsatisfiable 2CNFs
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
Parameterized Complexity
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A backbone of a propositional CNF formula is a variable whose truth value is the same in every truth assignment that satisfies the formula. The notion of backbones for CNF formulas has been studied in various contexts. In this paper, we introduce local variants of backbones, and study the computational complexity of detecting them. In particular, we consider k- backbones, which are backbones for sub-formulas consisting of at most k clauses, and iterative k- backbones, which are backbones that result after repeated instantiations of k- backbones. We determine the parameterized complexity of deciding whether a variable is a k- backbone or an iterative k- backbone for various restricted formula classes, including Horn, definite Horn, and Krom. We also present some first empirical results regarding backbones for CNF-Satisfiability (SAT). The empirical results we obtain show that a large fraction of the backbones of structured SAT instances are local, in contrast to random instances, which appear to have few local backbones.