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
A threshold for unsatisfiability
Journal of Computer and System Sciences
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
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
(2 +f(n))-SAT and its properties
Discrete Applied Mathematics - Discrete mathematics and theoretical computer science (DMTCS)
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The paper investigates the computational complexity of quantified Boolean formulas with fixed maximal deficiency. The satisfiability problem for quantified Boolean formulas with maximal deficiency 1 is shown to be solvable in polynomial time. For k=1, it is shown that true formulas with fixed maximal deficiency k have models in which all Boolean functions can be represented as CNF formulas over at most 2^4^k^/^3 universal variables. As a consequence, the satisfiability problem for QCNF formulas with fixed maximal deficiency is in NP and for fixed deficiency the minimal falsity problem is in D^P. For two subclasses of quantified Boolean formulas with PSPACE-complete evaluation problem, QEHORN and QE2-CNF , we show that for fixed deficiency the minimal falsity problem can be decided in polynomial time.