Polynomial-time recognition of minimal unsatisfiable formulas with fixed clause-variable difference
Theoretical Computer Science
NP-Completeness of Refutability by Literal-Once Resolution
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
On the structure of some classes of minimal unsatisfiable formulas
Discrete Applied Mathematics - The renesse issue on satisfiability
Lean clause-sets: generalizations of minimally unsatisfiable clause-sets
Discrete Applied Mathematics - The renesse issue on satisfiability
Homomorphisms of conjunctive normal forms
Discrete Applied Mathematics - The renesse issue on satisfiability
Formal methods for the validation of automotive product configuration data
Artificial Intelligence for Engineering Design, Analysis and Manufacturing
Minimal unsatisfiable formulas with bounded clause-variable difference are fixed-parameter tractable
Journal of Computer and System Sciences
Computing unsatisfiable k-SAT instances with few occurrences per variable
Theoretical Computer Science
MUP: a minimal unsatisfiability prover
Proceedings of the 2005 Asia and South Pacific Design Automation Conference
Computational complexity of quantified Boolean formulas with fixed maximal deficiency
Theoretical Computer Science
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
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
cmMUS: a tool for circumscription-based MUS membership testing
LPNMR'11 Proceedings of the 11th international conference on Logic programming and nonmonotonic reasoning
On variables with few occurrences in conjunctive normal forms
SAT'11 Proceedings of the 14th international conference on Theory and application of satisfiability testing
On minimal unsatisfiability and time-space trade-offs for k-DNF resolution
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
On deciding MUS membership with QBF
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
The local lemma is tight for SAT
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
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
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
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We consider the deficiency \math(F):=c(F) - n(F) and the maximal deficiency \math * (F) :=maxF1\math F \math(F) of a clause-set F (a conjunctive normal form), where c(F) is the number of clauses in F and n(F) is the number of variables.Combining ideas from matching and matroid theory with techniques from the area of resolution refutations, we prove that for clause-sets F with p\math * (F) \math k, where k is considered as a constant, the SAT problem, the minimally unsatisfiability problem and the MAXSAT problem are decidable in polynomial time (previously, only poly-time decidability of the minimally unsatisfiability problem was known, and that only for k = 1).