| | |
Summary: On the Maximum Satisfiability of Random Formulas
Dimitris Achlioptas
Department of Computer Science, University of California, Santa Cruz
optas@cs.ucsc.edu
Assaf Naor
Microsoft Research, Redmond, Washington
anaor@microsoft.com
Yuval Peres
Microsoft Research, Redmond, Washington
peres@stat.berkeley.edu
Abstract
Say that a k-CNF a formula is p-satisfiable if there exists a truth assignment satisfying a fraction
1 - 2-k
+ p 2-k
of its clauses (note that every k-CNF formula is 0-satisfiable). Let Fk(n, m) denote a
random k-CNF formula on n variables with m clauses. For every k 2 and every r > 0 we determine p
and = (k) = O(k2-k/2
) such that with probability tending to 1 as n , a random k-CNF formula
Fk(n, rn) is p-satisfiable but not (p + )-satisfiable.
1 Introduction
|
