Many hard examples for resolution
Journal of the ACM (JACM)
A threshold for unsatisfiability
Journal of Computer and System Sciences
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
Lower bounds for random 3-SAT via differential equations
Theoretical Computer Science - Phase transitions in combinatorial problems
Upper bounds on the satisfiability threshold
Theoretical Computer Science - Phase transitions in combinatorial problems
A note on random 2-SAT with prescribed literal degrees
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
The Asymptotic Order of the Random k -SAT Threshold
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Generating Satisfiable Problem Instances
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
The Probabilistic Analysis of a Greedy Satisfiability Algorithm
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
A backbone-search heuristic for efficient solving of hard 3-SAT formulae
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Balance and filtering in structured satisfiable problems
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
From High Girth Graphs to Hard Instances
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
Random SAT Instances à la Carte
Proceedings of the 2008 conference on Artificial Intelligence Research and Development: Proceedings of the 11th International Conference of the Catalan Association for Artificial Intelligence
Further investigations into regular XORSAT
AAAI'06 proceedings of the 21st national conference on Artificial intelligence - Volume 2
Generating hard SAT/CSP instances using expander graphs
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 3
Towards industrial-like random SAT instances
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
On the structure of industrial SAT instances
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
Discrete Applied Mathematics
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
Bounds on threshold of regular random k-SAT
SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
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We consider a model for generating random k-SAT formulas, in which each literal occurs approximately the same number of times in the formula clauses (regular random and k-SAT). Our experimental results show that such regular random k-SAT instances are much harder than the usual uniform random k-SAT problems. This is in agreement with other results that show that more balanced instances of random combinatorial problems are often much more difficult to solve than uniformly random instances, even at phase transition boundaries. There are almost no formal results known for such problem distributions. The balancing constraints add a dependency between variables that complicates a standard analysis. Regular random 3-SAT exhibits a phase transition as a function of the ratio 驴 of clauses to variables. The transition takes place at approximately 驴 = 3.5. We show that for 驴 3.78 with high probability (w.h.p.) random regular 3-SAT formulas are unsatisfiable. Specifically, the events $${\user1{\mathcal{E}}}_{n} $$ hold with high probability if Pr $${\left( {{\user1{\mathcal{E}}}_{n} } \right)} \to 1$$ when n 驴 驴. We also show that the analysis of a greedy algorithm proposed by Kaporis et al. for the uniform 3-SAT model can be adapted for regular random 3-SAT. In particular, we show that for formulas with ratio 驴