Minimal non-two-colorable hypergraphs and minimal unsatisfiable formulas
Journal of Combinatorial Theory Series A
Many hard examples for resolution
Journal of the ACM (JACM)
Enhancement schemes for constraint processing: backjumping, learning, and cutset decomposition
Artificial Intelligence
Intelligent backtracking on constraint satisfaction problems: experimental and theoretical results
Intelligent backtracking on constraint satisfaction problems: experimental and theoretical results
On the complexity of unsatisfiability proofs for random k-CNF formulas
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Hard problems for CSP Algorithms
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
Short proofs are narrow—resolution made simple
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
A sharp threshold in proof complexity
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Models and thresholds for random constraint satisfaction problems
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
The resolution complexity of constraint satisfaction
The resolution complexity of constraint satisfaction
Annals of Mathematics and Artificial Intelligence
Mick gets some (the odds are on his side) (satisfiability)
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
A comparison of ATMS and CSP techniques
IJCAI'89 Proceedings of the 11th international joint conference on Artificial intelligence - Volume 1
Where the really hard problems are
IJCAI'91 Proceedings of the 12th international joint conference on Artificial intelligence - Volume 1
Annals of Mathematics and Artificial Intelligence
The satisfiability threshold for randomly generated binary constraint satisfaction problems
Random Structures & Algorithms
Resolution complexity of random constraint satisfaction problems: another half of the story
Discrete Applied Mathematics - Special issue: Typical case complexity and phase transitions
Many hard examples in exact phase transitions
Theoretical Computer Science
Random constraint satisfaction: Easy generation of hard (satisfiable) instances
Artificial Intelligence
Consistency and random constraint satisfaction models
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
Resolution complexity of random constraint satisfaction problems: Another half of the story
Discrete Applied Mathematics
Exact thresholds for DPLL on random XOR-SAT and NP-complete extensions of XOR-SAT
Theoretical Computer Science
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Random instances are widely used as benchmarks in evaluating algorithms for finite-domain constraint satisfaction problems (CSPs). We present an analysis that shows why deciding satisfiability of instances from some distributions is challenging for current complete methods. For a typical random CSP model, we show that when constraints are not too tight almost all unsatisfiable instances have a structural property which guarantees that unsatisfiability proofs in a certain resolution-like system must be of exponential size. This proof system can efficiently simulate the reasoning of a large class of CSP algorithms which will thus have exponential running time on these instances.