On the critical exponents of random k-SAT
Random Structures & Algorithms
On the 2-Colorability of Random Hypergraphs
RANDOM '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
The threshold for random k-SAT is 2k (ln 2 - O(k))
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Linear phase transition in random linear constraint satisfaction problems
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Techniques from combinatorial approximation algorithms yield efficient algorithms for random 2k-SAT
Theoretical Computer Science
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
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
Regular Random k-SAT: Properties of Balanced Formulas
Journal of Automated Reasoning
Strong Refutation Heuristics for Random k-SAT
Combinatorics, Probability and Computing
On the maximum satisfiability of random formulas
Journal of the ACM (JACM)
Random constraint satisfaction: Easy generation of hard (satisfiable) instances
Artificial Intelligence
Foundations and Trends® in Theoretical Computer Science
Pairs of SAT-assignments in random Boolean formulæ
Theoretical Computer Science
Hiding satisfying assignments: two are better than one
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Generating hard satisfiable formulas by hiding solutions deceptiveily
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
Hiding satisfying assignments: two are better than one
Journal of Artificial Intelligence Research
Generating hard satisfiable formulas by hiding solutions deceptively
Journal of Artificial Intelligence Research
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
On the impact of small-world on local search
AI*IA'05 Proceedings of the 9th conference on Advances in Artificial Intelligence
5-regular graphs are 3-colorable with positive probability
ESA'05 Proceedings of the 13th annual European conference on Algorithms
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Form a random k-SAT formula on n variables by selecting uniformly and independently m = rn clauses out of all 2^k (_k^n ) possible k-clauses. The Satisfiability Threshold Conjecture asserts that for each k there exists a constant rk such that as n tends to infinity, the probability that the formula is satisfiable tends to 1 if r rk. It has long been known that 2 k/k 2k. We prove that rk 2k - 1 ln 2 - dk, where dk 驴 (1 + ln 2)/2. Our proof also allows a blurry glimpse of the "geometry" of the set of satisfying truth assignments.