On the probabilistic performance of algorithms for the satisfiability problem
Information Processing Letters
Probabilistic analysis of two heuristics for the 3-satisfiability problem
SIAM Journal on Computing
Discrete Applied Mathematics
Probabilistic performance of a heuristic for the satisfiability problem
Discrete Applied Mathematics
Information Sciences: an International Journal
Elimination of infrequent variables improves average case performance of satisfiability algorithms
SIAM Journal on Computing
Analysis of two simple heuristics on a random instance of k-SAT
Journal of Algorithms
Phase transitions and the search problem
Artificial Intelligence - Special volume on frontiers in problem solving: phase transitions and complexity
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
SIAM Journal on Computing
On the satisfiability and maximum satisfiability of random 3-CNF formulas
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
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
A machine program for theorem-proving
Communications of the ACM
Lower bounds for random 3-SAT via differential equations
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
Lower bounds for random 3-SAT via differential equations
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
Heuristic average-case analysis of the backtrack resolution of random 3-satisfiability instances
Theoretical Computer Science
Annals of Mathematics and Artificial Intelligence
Typical case complexity of satisfiability algorithms and the threshold phenomenon
Discrete Applied Mathematics - Special issue: Typical case complexity and phase transitions
The probabilistic analysis of a greedy satisfiability algorithm
Random Structures & Algorithms
Phase transition of multivariate polynomial systems
Mathematical Structures in Computer Science
Empirical hardness models: Methodology and a case study on combinatorial auctions
Journal of the ACM (JACM)
Typical case complexity of Satisfiability Algorithms and the threshold phenomenon
Discrete Applied Mathematics
Phase transition of multivariate polynomial systems
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
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
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We present a history of results related to the threhold phenomena which arise in the study of random conjunctive normal form (CNF) formulas. In a companion paper (D. Achlioptas, Theoret. Comput. Sci., this volume) the major ideas used to achieve many of the lower bounds results on the location of the threshold are described in an informal, intuitive manner.