Minimal non-two-colorable hypergraphs and minimal unsatisfiable formulas
Journal of Combinatorial Theory Series A
Graph minors. V. Excluding a planar graph
Journal of Combinatorial Theory Series B
Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
The complexity of facets resolved
Journal of Computer and System Sciences - 26th IEEE Conference on Foundations of Computer Science, October 21-23, 1985
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
An algorithm for the class of pure implicational formulas
Discrete Applied Mathematics - Special issue on the satisfiability problem and Boolean functions
Upper bounds to the clique width of graphs
Discrete Applied Mathematics
A machine program for theorem-proving
Communications of the ACM
On subclasses of minimal unsatisfiable formulas
Discrete Applied Mathematics - Special issue on Boolean functions and related problems
Discrete Applied Mathematics - Special issue on international workshop of graph-theoretic concepts in computer science WG'98 conference selected papers
Fixed-parameter complexity in AI and nonmonotonic reasoning
Artificial Intelligence
An efficient algorithm for the minimal unsatisfiability problem for a subclass of CNF
Annals of Mathematics and Artificial Intelligence
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
Satisfiability, Branch-Width and Tseitin Tautologies
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
The Quest for Efficient Boolean Satisfiability Solvers
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
An Upper Bound for Minimal Resolution Refutations
Proceedings of the 12th International Workshop on Computer Science Logic
An Application of Matroid Theory to the SAT Problem
COCO '00 Proceedings of the 15th Annual IEEE Conference on Computational Complexity
Lean clause-sets: generalizations of minimally unsatisfiable clause-sets
Discrete Applied Mathematics - The renesse issue on satisfiability
Improving a fixed parameter tractability time bound for the shadow problem
Journal of Computer and System Sciences - Special issue on Parameterized computation and complexity
Generalizations of Matched CNF Formulas
Annals of Mathematics and Artificial Intelligence
Parameterized Complexity
Matched formulas and backdoor sets
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
How many conflicts does it need to be unsatisfiable?
SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
A new bound for 3-satisfiable maxsat and its algorithmic application
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
Constraint satisfaction problems parameterized above or below tight bounds: a survey
The Multivariate Algorithmic Revolution and Beyond
On davis-putnam reductions for minimally unsatisfiable clause-sets
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
Fixed-parameter tractability of satisfying beyond the number of variables
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
Constraint Satisfaction Problems in Clausal Form I: Autarkies and Deficiency
Fundamenta Informaticae
On the Parameterized Complexity and Kernelization of the Workflow Satisfiability Problem
ACM Transactions on Information and System Security (TISSEC)
A new bound for 3-satisfiable MaxSat and its algorithmic application
Information and Computation
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Recognition of minimal unsatisfiable CNF formulas (unsatisfiable CNF formulas which become satisfiable if any clause is removed) is a classical Dp-complete problem. It was shown recently that minimal unsatisfiable formulas with n variables and n + k clauses can be recognized in time nO(k). We improve this result and present an algorithm with time complexity O(2kn4); hence the problem turns out to be fixed-parameter tractable (FTP) in the sense of Downey and Fellows (Parameterized Complexity, 1999).Our algorithm gives rise to a fixed-parameter tractable parameterization of the satisfiability problem: If for a given set of clauses F, the number of clauses in each of its subsets exceeds the number of variables occurring in the subset at most by k, then we can decide in time O(2kn3) whether F is satisfiable; k is called the maximum deficiency of F and can be efficiently computed by means of graph matching algorithms. Known parameters for fixed-parameter tractable satisfiability decision are tree-width or related to tree-width. Tree-width and maximum deficiency are incomparable in the sense that we can find formulas with constant maximum deficiency and arbitrarily high tree-width, and formulas where the converse prevails.