Generating hard satisfiability problems
Artificial Intelligence - Special volume on frontiers in problem solving: phase transitions and complexity
A threshold for unsatisfiability
Journal of Computer and System Sciences
Satisfiability threshold for random XOR-CNF formulas
Discrete Applied Mathematics - Special issue on the satisfiability problem and Boolean functions
Random 2-SAT and unsatisfiability
Information Processing Letters
Typical random 3-SAT formulae and the satisfiability threshold
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
The phase transition in 1-in-k SAT and NAE 3-SAT
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Complexity classifications of boolean constraint satisfaction problems
Complexity classifications of boolean constraint satisfaction problems
The scaling window of the 2-SAT transition
Random Structures & Algorithms
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
Approximating the Satisfiability Threshold for Random k-XOR-formulas
Combinatorics, Probability and Computing
Combinatorial sharpness criterion and phase transition classification for random CSPs
Information and Computation
The satisfiability threshold for randomly generated binary constraint satisfaction problems
Random Structures & Algorithms
A sharp threshold for the renameable-Horn and the q-Horn properties
Discrete Applied Mathematics - Special issue: Typical case complexity and phase transitions
Typical case complexity of satisfiability algorithms and the threshold phenomenon
Discrete Applied Mathematics - Special issue: Typical case complexity and phase transitions
Threshold properties of random boolean constraint satisfaction problems
Discrete Applied Mathematics - Special issue: Typical case complexity and phase transitions
Threshold properties of random boolean constraint satisfaction problems
Discrete Applied Mathematics
A sharp threshold for the renameable-Horn and the q-Horn properties
Discrete Applied Mathematics
Typical case complexity of Satisfiability Algorithms and the threshold phenomenon
Discrete Applied Mathematics
On the phase transitions of random k-constraint satisfaction problems
Artificial Intelligence
Exact thresholds for DPLL on random XOR-SAT and NP-complete extensions of XOR-SAT
Theoretical Computer Science
Constraint Satisfaction Problems in Clausal Form I: Autarkies and Deficiency
Fundamenta Informaticae
A general model and thresholds for random constraint satisfaction problems
Artificial Intelligence
An algorithm for random signed 3-SAT with intervals
Theoretical Computer Science
| Hi-index | 5.23 |
We develop a probabilistic model on the generalized satisfiability problems defined by Schaefer (in: Proceedings of the 10th STOC, San Diego, CA, USA, Association for Computing Machinery, New York, 1978, pp. 216-226) for which the arity of the constraints is fixed in order to study the associated phase transition. We establish new results on minimal elements associated with such generalized satisfiability problems. These results are the keys of the exploration we conduct on the location and on the nature of the phase transition for generalized satisfiability. We first prove that the phase transition occurs at the same scale for every reasonable problem and we provide lower and upper bounds for the associated critical ratio. Our framework allows one to get these bounds in a uniform way, in particular, we obtain a lower bound proportional to the number of variables for k-SAT without analyzing any algorithm. Finally, we reveal the seed of coarseness for the phase transition of generalized satisfiability: 2-XOR-SAT.