Summary: On smoothed k-CNF formulas and the Walksat algorithm
Amin Coja-Oghlan
Uriel Feige
Alan Frieze
Michael Krivelevich§
Dan Vilenchik¶
Abstract
In this paper we study the model of -smoothed k-
CNF formulas. Starting from an arbitrary instance
F with n variables and m = dn clauses, apply the -
smoothing operation of flipping the polarity of every
literal in every clause independently at random with
probability . Keeping and k fixed, and letting the
density d = m/n grow, it is rather easy to see that
for d -k
ln 2, F becomes whp unsatisfiable after
smoothing.
We show that a lower density that behaves
roughly like -k+1
suffices for this purpose. We also

Source: Applebaum, Benny - Faculty of Mathematics and Computer Science, Weizmann Institute of Science

Collections: Computer Technologies and Information Sciences