Probabilistic analysis of two heuristics for the 3-satisfiability problem
SIAM Journal on Computing
Many hard examples for resolution
Journal of the ACM (JACM)
Information Sciences: an International Journal
Analysis of two simple heuristics on a random instance of k-SAT
Journal of Algorithms
Generating hard satisfiability problems
Artificial Intelligence - Special volume on frontiers in problem solving: phase transitions and complexity
Experimental results on the crossover point in random 3-SAT
Artificial Intelligence - Special volume on frontiers in problem solving: phase transitions and complexity
Sudden emergence of a giant k-core in a random graph
Journal of Combinatorial Theory Series B
A threshold for unsatisfiability
Journal of Computer and System Sciences
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
2+p-SAT: relation of typical-case complexity to the nature of the phase transition
Random Structures & Algorithms - Special issue on statistical physics methods in discrete probability, combinatorics, and theoretical computer science
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
A machine program for theorem-proving
Communications of the ACM
Short proofs are narrow—resolution made simple
Journal of the ACM (JACM)
Rigorous results for random (2 + p)-SAT
Theoretical Computer Science - Phase transitions in combinatorial problems
Lower bounds for random 3-SAT via differential equations
Theoretical Computer Science - Phase transitions in combinatorial problems
Constructing an asymptotic phase transition in random binary constraint satisfaction problems
Theoretical Computer Science - Phase transitions in combinatorial problems
An exponential separation between regular and general resolution
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
On the Relative Complexity of Resolution Refinements and Cutting Planes Proof Systems
SIAM Journal on Computing
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Resolution Complexity of Random Constraints
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
A probabilistic analysis of randomly generated binary constraint satisfaction problems
Theoretical Computer Science
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Generalized satisfiability problems: minimal elements and phase transitions
Theoretical Computer Science
A sharp threshold in proof complexity yields lower bounds for satisfiability search
Journal of Computer and System Sciences - STOC 2001
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Random k-Sat: A Tight Threshold For Moderately Growing k
Combinatorica
Cores in random hypergraphs and Boolean formulas
Random Structures & Algorithms
Threshold values of random K-SAT from the cavity method
Random Structures & Algorithms
The satisfiability threshold for randomly generated binary constraint satisfaction problems
Random Structures & Algorithms
Many hard examples in exact phase transitions
Theoretical Computer Science
Random $k$-SAT: Two Moments Suffice to Cross a Sharp Threshold
SIAM Journal on Computing
The Resolution Complexity of Random Constraint Satisfaction Problems
SIAM Journal on Computing
The k-core and branching processes
Combinatorics, Probability and Computing
Mick gets some (the odds are on his side) (satisfiability)
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
When does the giant component bring unsatisfiability?
Combinatorica
Exact phase transitions in random constraint satisfaction problems
Journal of Artificial Intelligence Research
Understanding the power of clause learning
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Hard and easy distributions of SAT problems
AAAI'92 Proceedings of the tenth national conference on Artificial intelligence
Threshold phenomena in random constraint satisfaction problems
Threshold phenomena in random constraint satisfaction problems
Hi-index | 5.23 |
This paper discusses a model of constraint satisfaction problems known as uniquely extendible constraint satisfaction problems. This model includes and generalizes XOR-SAT, and the model includes an NP-complete problem that appears to share many of the threshold characteristics of random SAT. In this paper we find an exact threshold in the behavior of two versions of DPLL on random instances of this problem. One version uses the unit clause heuristic, and the other uses the generalized unit clause heuristic. Specifically, for DPLL with the unit clause heuristic, we prove that there is a clause density c, smaller than the satisfiability threshold, such that for random instances with density smaller than this threshold, DPLL with unit clause will find a satisfying assignment in linear time, with uniformly positive probability. However, for random instances with density larger than this threshold, DPLL with unit clause will require exponential time, with uniformly positive probability, to find a satisfying assignment. We then find the equivalent threshold density for DPLL with the generalized unit clause heuristic. We also prove the analog of the (2+p)-SAT Conjecture for this class of problems.