Minimal non-two-colorable hypergraphs and minimal unsatisfiable formulas
Journal of Combinatorial Theory Series A
On subclasses of minimal unsatisfiable formulas
Discrete Applied Mathematics - Special issue on Boolean functions and related problems
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
Generalizations of Matched CNF Formulas
Annals of Mathematics and Artificial Intelligence
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
Minimal unsatisfiable formulas with bounded clause-variable difference are fixed-parameter tractable
Journal of Computer and System Sciences
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Solving #SAT using vertex covers
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
Parameterized Complexity
Backdoor Sets of Quantified Boolean Formulas
Journal of Automated Reasoning
Computation of renameable Horn backdoors
SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
A new bound for an NP-hard subclass of 3-SAT using backdoors
SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
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We study parameterizations of the satisfiability problem for propositional formulas in conjunctive normal form. In particular, we consider two parameters that generalize the notion of matched formulas: (i) the well studied parameter maximum deficiency, and (ii) the size of smallest backdoor sets with respect to certain base classes of bounded maximum deficiency. The simplest base class considered is the class of matched formulas. Our main technical contribution is a hardness result for the detection of weak, strong, and deletion backdoor sets. This result implies, subject to a complexity theoretic assumption, that small backdoor sets with respect to the base classes under consideration cannot be found significantly faster than by exhaustive search.