 
Summary: JOURNAL OF THE
AMERICAN MATHEMATICAL SOCIETY
Volume 17, Number 4, Pages 947973
S 08940347(04)004643
Article electronically published on August 27, 2004
THE THRESHOLD FOR RANDOM kSAT IS 2k
log 2  O(k)
DIMITRIS ACHLIOPTAS AND YUVAL PERES
1. Introduction
Call a disjunction of k Boolean variables a kclause. For a set V of n Boolean
variables, let Ck(V ) denote the set of all 2k
nk
possible kclauses on V . A random
kCNF formula Fk(n, m) is formed by selecting uniformly, independently and with
replacement m clauses from Ck and taking their conjunction.1
The study of such
random kCNF formulas has attracted substantial interest in logic, optimization,
combinatorics, the theory of algorithms and, more recently, statistical physics.
We will say that a sequence of events En occurs with high probability (w.h.p.) if
limn P[En] = 1 and with uniformly positive probability if lim infn P[En] > 0.
