Probabilistic analysis of two heuristics for the 3-satisfiability problem
SIAM Journal on Computing
Information Sciences: an International Journal
Analysis of two simple heuristics on a random instance of k-SAT
Journal of Algorithms
A threshold for unsatisfiability
Journal of Computer and System Sciences
A critical point for random graphs with a given degree sequence
Random Graphs 93 Proceedings of the sixth international seminar on Random graphs and probabilistic methods in combinatorics and computer science
On the satisfiability and maximum satisfiability of random 3-CNF formulas
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Setting 2 variables at a time yields a new lower bound for random 3-SAT (extended abstract)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Results related to threshold phenomena research in satisfiability: lower bounds
Theoretical Computer Science - Phase transitions in combinatorial problems
The analysis of a list-coloring algorithm on a random graph
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Optimal myopic algorithms for random 3-SAT
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third 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
Results related to threshold phenomena research in satisfiability: lower bounds
Theoretical Computer Science - Phase transitions in combinatorial problems
Upper bounds on the satisfiability threshold
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
The Probabilistic Analysis of a Greedy Satisfiability Algorithm
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
On sufficient conditions for unsatisfiability of random formulas
Journal of the ACM (JACM)
Exponential bounds for DPLL below the satisfiability threshold
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
A sharp threshold in proof complexity yields lower bounds for satisfiability search
Journal of Computer and System Sciences - STOC 2001
On the design of distributed protocols from differential equations
Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
Heuristic average-case analysis of the backtrack resolution of random 3-satisfiability instances
Theoretical Computer Science
Annals of Mathematics and Artificial Intelligence
Phase transition in a random NK landscape model
GECCO '05 Proceedings of the 7th annual conference on Genetic and evolutionary computation
Threshold values of random K-SAT from the cavity method
Random Structures & Algorithms
Typical case complexity of satisfiability algorithms and the threshold phenomenon
Discrete Applied Mathematics - Special issue: Typical case complexity and phase transitions
Resolution complexity of random constraint satisfaction problems: another half of the story
Discrete Applied Mathematics - Special issue: Typical case complexity and phase transitions
The probabilistic analysis of a greedy satisfiability algorithm
Random Structures & Algorithms
Regular Random k-SAT: Properties of Balanced Formulas
Journal of Automated Reasoning
Phase transitions of PP-complete satisfiability problems
Discrete Applied Mathematics
A continuous–discontinuous second-order transition in the satisfiability of random Horn-SAT formulas
Random Structures & Algorithms
Phase transition in a random NK landscape model
Artificial Intelligence
Empirical hardness models: Methodology and a case study on combinatorial auctions
Journal of the ACM (JACM)
Hiding satisfying assignments: two are better than one
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Hiding satisfying assignments: two are better than one
Journal of Artificial Intelligence Research
An analysis of phase transition in NK landscapes
Journal of Artificial Intelligence Research
Resolution complexity of random constraint satisfaction problems: Another half of the story
Discrete Applied Mathematics
Typical case complexity of Satisfiability Algorithms and the threshold phenomenon
Discrete Applied Mathematics
Approximation algorithm for random MAX-kSAT
SAT'04 Proceedings of the 7th international conference on Theory and Applications of Satisfiability Testing
Observed lower bounds for random 3-SAT phase transition density using linear programming
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
A generating function method for the average-case analysis of DPLL
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
A continuous-discontinuous second-order transition in the satisfiability of random Horn-SAT formulas
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Exact thresholds for DPLL on random XOR-SAT and NP-complete extensions of XOR-SAT
Theoretical Computer Science
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
Some heuristic analysis of local search algorithms for SAT problems
SAGA'05 Proceedings of the Third international conference on StochasticAlgorithms: foundations and applications
An analysis of one-dimensional schelling segregation
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Survey: The cook-book approach to the differential equation method
Computer Science Review
Exponential lower bounds for DPLL algorithms on satisfiable random 3-CNF formulas
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
Unsatisfiability bounds for random CSPs from an energetic interpolation method
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
An algorithm for random signed 3-SAT with intervals
Theoretical Computer Science
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It is widely believed that the probability of satisfiability for random k-SAT formulae exhibits a sharp threshold as a function of their clauses-to-variables ratio. For the most studied case, k= 3, there have been a number of results during the last decade providing upper and lower bounds for the threshold's potential location. All lower bounds in this vein have been algorithmic, i.e., in each case a particular algorithm was shown to satisfy random instances of 3-SAT with probability 1- o(1) if the clauses-to-variables ratio is below a certain value. We show how differential equations can serve as a generic tool for analyzing such algorithms by rederiving most of the known lower bounds for random 3-SAT in a simple, uniform manner.