Tail bounds for occupancy and the satisfiability threshold conjecture
Random Structures & Algorithms
A general upper bound for the satisfiability threshold of random r-SAT formulae
Journal of Algorithms
Approximating the unsatisfiability threshold of random formulas
Random Structures & Algorithms
Typical random 3-SAT formulae and the satisfiability threshold
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
On the solution-space geometry of random constraint satisfaction problems
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Regular Random k-SAT: Properties of Balanced Formulas
Journal of Automated Reasoning
A new look at survey propagation and its generalizations
Journal of the ACM (JACM)
The unsatisfiability threshold revisited
Discrete Applied Mathematics
On the satisfiability threshold and clustering of solutions of random 3-SAT formulas
Theoretical Computer Science
On the satisfiability threshold of formulas with three literals per clause
Theoretical Computer Science
Non uniform selection of solutions for upper bounding the 3-SAT threshold
SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
Sensitivity of Boolean formulas
European Journal of Combinatorics
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The problem of estimating the proportion of satisfiable instances of a given CSP (constraint satisfaction problem) can be tackled through weighting. It consists in putting onto each solution a non-negative real value based on its neighborhood in a way that the total weight is at least 1 for each satisfiable instance. We define in this paper a general weighting scheme for the estimation of satisfiability of general CSPs. First we give some sufficient conditions for a weighting system to be correct. Then we show that this scheme allows for an improvement on the upper bound on the existence of non-trivial cores in 3-SAT obtained by Maneva and Sinclair (2008) [17] to 4.419. Another more common way of estimating satisfiability is ordering. This consists in putting a total order on the domain, which induces an orientation between neighboring solutions in a way that prevents circuits from appearing, and then counting only minimal elements. We compare ordering and weighting under various conditions.