 
Summary: Setting 2 variables at a time yields a new lower bound
for random 3SAT
[ExtendedAbstract]
Dimitris Achlioptas
MicrosoftResearch
One MicrosoftWay
Redmond,WA98052
optas@rnicrosoft.com
ABSTRACT
Let X be a set of n Boolean variables and denote by C(X)
the set of all 3clauses over X, i.e. the set of all 8(3) possible
disjunctions of three distinct, noncomplementary literais
from variables in X. Let F(n, m) be a random 3SAT 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.
