 
Summary: Exponential Bounds for DPLL Below the Satisfiability Threshold
Dimitris Achlioptas
Paul Beame
Michael Molloy
Abstract
For each k 4, we give rk > 0 such that a random
kCNF formula F with n variables and rkn clauses
is satisfiable with high probability, but ordereddll
takes exponential time on F with uniformly positive
probability. Using results of [2], this can be strength
ened to a high probability result for certain natu
ral backtracking schemes and extended to many other
DPLL algorithms.
1 Previous work
In the last twenty years a significant amount of work
has been devoted to the study of randomly generated
satisfiability instances and the performance of different
algorithms on them. Historically, a major motivation
for studying random instances has been the desire to
understand the hardness of "typical" instances. Indeed,
