Probabilistic analysis of two heuristics for the 3-satisfiability problem
SIAM Journal on Computing
Approximating the unsatisfiability threshold of random formulas
Random Structures & Algorithms
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
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
Random $k$-SAT: Two Moments Suffice to Cross a Sharp Threshold
SIAM Journal on Computing
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
Empirical hardness models: Methodology and a case study on combinatorial auctions
Journal of the ACM (JACM)
Data reductions, fixed parameter tractability, and random weighted d-CNF satisfiability
Artificial Intelligence
Average-case analysis for the MAX-2SAT problem
Theoretical Computer Science
Speeding-up non-clausal local search for propositional satisfiability with clause learning
SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
Average-case analysis for the MAX-2SAT problem
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
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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 consists of random k- SAT formulas whose clauses are chosen uniformly from among all clauses satisfying some randomly chosen truth assignment A. Unfortunately, instances generated in this manner tend to be relatively easy and can be solved efficiently by practical heuristics. Roughly speaking, for a number of different algorithms, A acts as a stronger and stronger attractor as the formula's density increases. Motivated by recent results on the geometry of the space of satisfying truth assignments of random k-SAT and NAE-k-SAT formulas, we introduce a simple twist on this basic model, which appears to dramatically increase its hardness. 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 algorithms to find any truth assignment. We give theoretical and experimental evidence supporting this assertion.