Probabilistic analysis of two heuristics for the 3-satisfiability problem
SIAM Journal on Computing
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 general upper bound for the satisfiability threshold of random r-SAT formulae
Journal of Algorithms
Length of prime implicants and number of solutions of random CNF formulae
Theoretical Computer Science
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
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
Uniform boundedness of critical crossing probabilities implies hyperscaling
Random Structures & Algorithms - Special issue on statistical physics methods in discrete probability, combinatorics, and theoretical computer science
A Treshold for Unsatisfiability
MFCS '92 Proceedings of the 17th International Symposium on Mathematical Foundations of Computer Science
Survey: The cook-book approach to the differential equation method
Computer Science Review
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In the random 2-SAT problem, we are given a set C of m disjunctions of two literals chosen at random within the ( 2n2 ) pairs of distinct literals coming from n logical variables. The basic problem is to /nd out for which values of the ratio _=m=n the disjunctions in C are almost surely simultaneously satisfiable (or almost surely not simultaneously satisfiable) as n tends to infinity. The purpose of this paper is to review the main steps in the solution of this problem, starting with the location of the asymptotic critical ratio around 8 years ago and ending with the recent almost complete solution due to Bollob4as et al. Thus, this paper is not a review in the usual sense of the word, i.e., it does not include all the known results about random 2-SAT. We will also make a few comments concerning the behaviour of the number of satisfying assignments of random instances of 2-SAT below the critical ratio, a problem relevant to theoretical physics.