Probabilistic analysis of two heuristics for the 3-satisfiability problem
SIAM Journal on Computing
A sharp threshold in proof complexity
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
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
Generating Satisfiable Problem Instances
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
The threshold for random k-SAT is 2k (ln 2 - O(k))
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Heuristic average-case analysis of the backtrack resolution of random 3-satisfiability instances
Theoretical Computer Science
Hiding satisfying assignments: two are better than one
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Balance and filtering in structured satisfiable problems
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Protecting data privacy through hard-to-reverse negative databases
ISC'06 Proceedings of the 9th international conference on Information Security
Classifying and clustering in negative databases
Frontiers of Computer Science: Selected Publications from Chinese Universities
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To test incomplete search algorithms for constraint satisfaction problems such as 3-SAT, we need a source of hard, but satisfiable, benchmark instances. A simple way to do this is to choose a random truth assignment A, and then choose clauses randomly from among those satisfied by A. However, this method tends to produce easy problems, since the majority of literals point toward the "hidden" assignment A. Last year, (Achlioptas, Jia, & Moore 2004) proposed a problem generator that cancels this effect by hiding both A and its complement A. While the resulting formulas appear to be just as hard for DPLL algorithms as random 3-SAT formulas with no hidden assignment, they can be solved by WalkSAT in only polynomial time. Here we propose a new method to cancel the attraction to A, by choosing a clause with t 0 literals satisfied by A with probability proportional to qt for some q q, we can generate formulas whose variables have no bias, i.e., which are equally likely to be true or false; we can even cause the formula to "deceptively" point away from A. We present theoretical and experimental results suggesting that these formulas are exponentially hard both for DPLL algorithms and for incomplete algorithms such as WalkSAT.