Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
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
Bounding the unsatisfiability threshold of random 3-SAT
Random Structures & Algorithms
On the solution-space geometry of random constraint satisfaction problems
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
The probabilistic analysis of a greedy satisfiability algorithm
Random Structures & Algorithms
The unsatisfiability threshold revisited
Discrete Applied Mathematics
On the satisfiability threshold of formulas with three literals per clause
Theoretical Computer Science
Discrete Applied Mathematics
Survey: The cook-book approach to the differential equation method
Computer Science Review
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
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We study the structure of satisfying assignments of a random 3-Sat formula. In particular, we show that a random formula of density @a=4.453 almost surely has no non-trivial ''core'' assignments. Core assignments are certain partial assignments that can be extended to satisfying assignments, and have been studied recently in connection with the Survey Propagation heuristic for random Sat. Their existence implies the presence of clusters of solutions, and they have been shown to exist with high probability below the satisfiability threshold for k-Sat with k=9 [D. Achlioptas, F. Ricci-Tersenghi, On the solution-space geometry of random constraint satisfaction problems, in: Proc. 38th ACM Symp. Theory of Computing, STOC, 2006, pp. 130-139]. Our result implies that either this does not hold for 3-Sat, or the threshold density for satisfiability in 3-Sat lies below 4.453. The main technical tool that we use is a novel simple application of the first moment method.