Many hard examples for resolution
Journal of the ACM (JACM)
On the complexity of unsatisfiability proofs for random k-CNF formulas
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Short proofs are narrow—resolution made simple
Journal of the ACM (JACM)
A sharp threshold in proof complexity
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Constructing an asymptotic phase transition in random binary constraint satisfaction problems
Theoretical Computer Science - Phase transitions in combinatorial problems
Models and thresholds for random constraint satisfaction problems
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Efficient conflict driven learning in a boolean satisfiability solver
Proceedings of the 2001 IEEE/ACM international conference on Computer-aided design
A perspective on certain polynomial-time solvable classes of satisfiability
Discrete Applied Mathematics
Resolution Complexity of Random Constraints
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
The resolution complexity of constraint satisfaction
The resolution complexity of constraint satisfaction
The Resolution Complexity of Random Constraint Satisfaction Problems
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Graph Theory With Applications
Graph Theory With Applications
The resolution complexity of random graphk-colorability
Discrete Applied Mathematics - Special issue: Typical case complexity and phase transitions
Exact phase transitions in random constraint satisfaction problems
Journal of Artificial Intelligence Research
Heuristics based on unit propagation for satisfiability problems
IJCAI'97 Proceedings of the 15th international joint conference on Artifical intelligence - Volume 1
Data reductions, fixed parameter tractability, and random weighted d-CNF satisfiability
Artificial Intelligence
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
Random instances of W[2]-complete problems: thresholds, complexity, and algorithms
SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
On the phase transitions of random k-constraint satisfaction problems
Artificial Intelligence
A note on treewidth in random graphs
COCOA'11 Proceedings of the 5th international conference on Combinatorial optimization and applications
Generating highly balanced sudoku problems as hard problems
Journal of Heuristics
Large hinge width on sparse random hypergraphs
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
A general model and thresholds for random constraint satisfaction problems
Artificial Intelligence
Variable-Centered Consistency in Model RB
Minds and Machines
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In this paper, we study the possibility of designing non-trivial random CSP models by exploiting the intrinsic connection between structures and typical-case hardness. We show that constraint consistency, a notion that has been developed to improve the efficiency of CSP algorithms, is in fact the key to the design of random CSP models that have interesting phase transition behavior and guaranteed exponential resolution complexity without putting much restriction on the parameter of constraint tightness or the domain size of the problem. We propose a very flexible framework for constructing problem instances with interesting behavior and develop a variety of concrete methods to construct specific random CSP models that enforce different levels of constraint consistency. A series of experimental studies with interesting observations are carried out to illustrate the effectiveness of introducing structural elements in random instances, to verify the robustness of our proposal, and to investigate features of some specific models based on our framework that are highly related to the behavior of backtracking search algorithms.