Solving dense subset-sum problems by using analytical number theory
Journal of Complexity
New analytical results in subset-sum problem
Discrete Mathematics - Special issue on combinatorics and algorithms
Analysis of two simple heuristics on a random instance of k-SAT
Journal of Algorithms
Experimental results on the crossover point in random 3-SAT
Artificial Intelligence - Special volume on frontiers in problem solving: phase transitions and complexity
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
On the satisfiability and maximum satisfiability of random 3-CNF formulas
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Setting 2 variables at a time yields a new lower bound for random 3-SAT (extended abstract)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Typical random 3-SAT formulae and the satisfiability threshold
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
2+p-SAT: relation of typical-case complexity to the nature of the phase transition
Random Structures & Algorithms - Special issue on statistical physics methods in discrete probability, combinatorics, and theoretical computer science
Bounding the unsatisfiability threshold of random 3-SAT
Random Structures & Algorithms
The scaling window of the 2-SAT transition
Random Structures & Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A Treshold for Unsatisfiability
MFCS '92 Proceedings of the 17th International Symposium on Mathematical Foundations of Computer Science
Optimal myopic algorithms for random 3-SAT
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
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The SAT problem is one of the basic problems from complexity theory. When SAT is restricted to clauses of length k, we obtain the so-called k-SAT problem. For k ≥ 3, it is a NP-complete problem but it is believed that most of the instances are easy to solve. In fact, numerical evidence shows that a threshold phenomenon is to be expected. Up to now only upper bounds and lower bounds of the prospective value of the transition point have been obtained. Concerning lower bounds, they are obtained by considering special algorithms for which we can prove that it solves almost all instances of k-SAT if the ratio of the number of clauses by the number of variables is less than some given value.In this expository paper, we propose a completely new approach on the problem of evaluating from below the prospective value of the transition point by showing a connection between k-SAT and number theory. More precisely, it is based on additive number theoretic considerations and avoids the use of any specific algorithm by directly counting the number of solutions to a system encoding an instance of k-SAT.