Minimal non-two-colorable hypergraphs and minimal unsatisfiable formulas
Journal of Combinatorial Theory Series A
On the r,s satisfiability problem and a conjecture of Tovey
Discrete Applied Mathematics
DNF tautologies with a limited number of occurences of every variable
Theoretical Computer Science
An efficient algorithm for the minimal unsatisfiability problem for a subclass of CNF
Annals of Mathematics and Artificial Intelligence
An Application of Matroid Theory to the SAT Problem
COCO '00 Proceedings of the 15th Annual IEEE Conference on Computational Complexity
On the structure of some classes of minimal unsatisfiable formulas
Discrete Applied Mathematics - The renesse issue on satisfiability
Homomorphisms of conjunctive normal forms
Discrete Applied Mathematics - The renesse issue on satisfiability
Deciding relaxed two-colorability: a hardness jump
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
The local lemma is tight for SAT
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
| Hi-index | 5.23 |
(k, s)-SAT is the propositional satisfiability problem restricted to instances where each clause has exactly k distinct literals and every variable occurs at most s times. It is known that there exists an exponential function f such that for s ≤ f(k) all (k, s)-SAT instances are satisfiable, but (k, f (k) + 1)- SAT is already NP-complete (k ≥ 3). Exact values of f are only known for k = 3 and 4, and it is open whether f is computable. We introduce a computable function f1 which bounds f from above and determine the values of f1 by means of a calculus of integer sequences. This new approach enables us to improve the best known upper bounds for f(k), generalizing the known constructions for unsatisfiable (k, s)-SAT instances for small k.