Probabilistic analysis of two heuristics for the 3-satisfiability problem
SIAM Journal on Computing
Phase transitions and the search problem
Artificial Intelligence - Special volume on frontiers in problem solving: phase transitions and complexity
Approximating the unsatisfiability threshold of random formulas
Random Structures & Algorithms
A sharp threshold in proof complexity
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Lower bounds for random 3-SAT via differential equations
Theoretical Computer Science - Phase transitions in combinatorial problems
Almost all graphs with average degree 4 are 3-colorable
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
The Asymptotic Order of the Random k -SAT Threshold
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Using Walk-SAT and Rel-Sat for Cryptographic Key Search
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
Generating Satisfiable Problem Instances
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
Heuristics based on unit propagation for satisfiability problems
IJCAI'97 Proceedings of the 15th international joint conference on Artifical intelligence - Volume 1
Balance and filtering in structured satisfiable problems
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Evolving combinatorial problem instances that are difficult to solve
Evolutionary Computation
Random constraint satisfaction: Easy generation of hard (satisfiable) instances
Artificial Intelligence
Generating Satisfiable SAT Instances Using Random Subgraph Isomorphism
Canadian AI '09 Proceedings of the 22nd Canadian Conference on Artificial Intelligence: Advances in Artificial Intelligence
Generating hard satisfiable formulas by hiding solutions deceptiveily
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
Generating hard satisfiable formulas by hiding solutions deceptively
Journal of Artificial Intelligence Research
A simple model to generate hard satisfiable instances
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Challenging heuristics: evolving binary constraint satisfaction problems
Proceedings of the 14th annual conference on Genetic and evolutionary computation
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The evaluation of incomplete satisfiability solvers depends critically on the availability of hard satisfiable instances. A plausible source of such instances are k-CNF formulas whose clauses are chosen uniformly at random among all clauses satisfying some randomly chosen truth assignment A. Unfortunately, instances generated in this manner are relatively easy and can be solved efficiently by practical heuristics. Roughly speaking, as the number of clauses is increased, A acts as a stronger and stronger attractor. Motivated by recent results on the geometry of the space of solutions for random k-SAT and NAE-k-SAT instances, we propose a very simple twist on this model that greatly increases the hardness of the resulting formulas. Namely, in addition to forbidding the clauses violated by the hidden assignment A, we also forbid the clauses violated by its complement, so that both A and A are satisfying. It appears that under this "symmetrization" the effects of the two attractors largely cancel out, making it much harder for an algorithm to "feel" (and find) either one. We give theoretical and experimental evidence supporting this assertion.