Minimal non-two-colorable hypergraphs and minimal unsatisfiable formulas
Journal of Combinatorial Theory Series A
The complexity of facets resolved
Journal of Computer and System Sciences - 26th IEEE Conference on Foundations of Computer Science, October 21-23, 1985
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
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
Matching Theory (North-Holland mathematics studies)
Matching Theory (North-Holland mathematics studies)
Solving satisfiability in less than 2n steps
Discrete Applied Mathematics
Parameterized Complexity
Generalizations of Matched CNF Formulas
Annals of Mathematics and Artificial Intelligence
MUP: a minimal unsatisfiability prover
Proceedings of the 2005 Asia and South Pacific Design Automation Conference
Faster exact solving of SAT formulae with a low number of occurrences per variable
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
Hi-index | 0.00 |
Recognition of minimal unsatisfiable CNF formulas (unsatisfiable CNF formulas which become satisfiable by removing any clause) is NP-hard; 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(2k n4) --hence the problem turns out to be fixed-parameter tractable (FTP) in the sense of Downey and Fellows (Parameterized Complexity, Springer Verlag, 1999). Our algorithm gives rise to an FPT parameterization of SAT ("maximum deficiency") which is incomparable with known FPT parameterizations of SAT like tree-width.