Summary: Setting 2 variables at a time yields a new lower bound
for random 3-SAT
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 for-
mula formed by selecting, with replacement, m clauses uni-
formly at random from C(X) and taking their conjunction.
The satisfiabili~y threshold conjecture asserts that there ex-
ists a constant ra such that as n --+ cą, F(n, rn) is satisfiable
with probability that tends to 1 if r < ra, but unsatisfiable
with probability that tends to 1 if r :> r3. Experimental
evidence suggests rz ~ 4.2.