On functional dependencies in q-Horn theories
Artificial Intelligence
Some interesting research directions in satisfiability
Annals of Mathematics and Artificial Intelligence
Why is Combinational ATPG Efficiently Solvable for Practical VLSI Circuits?
Journal of Electronic Testing: Theory and Applications
A perspective on certain polynomial-time solvable classes of satisfiability
Discrete Applied Mathematics
Finding Tractable Formulas in NNF
CL '00 Proceedings of the First International Conference on Computational Logic
A complete adaptive algorithm for propositional satisfiability
Discrete Applied Mathematics
Lean clause-sets: generalizations of minimally unsatisfiable clause-sets
Discrete Applied Mathematics - The renesse issue on satisfiability
Solving the Resolution-Free SAT Problem by Submodel Propagation in Linear Time
Annals of Mathematics and Artificial Intelligence
A sharp threshold for the renameable-Horn and the q-Horn properties
Discrete Applied Mathematics - Special issue: Typical case complexity and phase transitions
Typical case complexity of satisfiability algorithms and the threshold phenomenon
Discrete Applied Mathematics - Special issue: Typical case complexity and phase transitions
A sharp threshold for the renameable-Horn and the q-Horn properties
Discrete Applied Mathematics
Typical case complexity of Satisfiability Algorithms and the threshold phenomenon
Discrete Applied Mathematics
Finding models for blocked 3-SAT problems in linear time by systematical refinement of a sub-model
KI'06 Proceedings of the 29th annual German conference on Artificial intelligence
On the boolean connectivity problem for horn relations
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
On the Boolean connectivity problem for Horn relations
Discrete Applied Mathematics
Observed lower bounds for random 3-SAT phase transition density using linear programming
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
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This paper associates a linear programming problem (LP) to any conjunctive normal form $\gf$, and shows that the optimum value $Z(\gf)$ of this LP measures the complexity of the corresponding SAT (Boolean satisfiability) problem. More precisely, there is an algorithm for SAT that runs in polynomial time on the class of satisfiability problems satisfying $Z(\gf)\leq 1+\frac{c\log n}{n}$ for a fixed constant $c$, where $n$ is the number of variables. In contrast, for any fixed $\betaSAT is still NP complete when restricted to the class of CNFs for which $Z(\gf)\leq 1+(1/n^{\beta})$.