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Let X be a set of n Boolean variables and denote by C(X) the set of all 3-clauses over X, i.e. the set of all 8(3 ) possible disjunctions of three distinct, non-complementary literais from variables in X. Let F(n, m) be a random 3-SAT formula formed by selecting, with replacement, m clauses uniformly at random from C(X) and taking their conjunction. The satisfiabili~y threshold conjecture asserts that there exists a constant ra such that as n --+ c¢, F(n, rn) is satisfiable with probabilitydoi:10.1145/335305.335309 dblp:conf/stoc/Achlioptas00 fatcat:2fqmfoyhxfbxtkakmazhswgi7y