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JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY
 

Summary: JOURNAL OF THE
AMERICAN MATHEMATICAL SOCIETY
Volume 17, Number 4, Pages 947973
S 0894-0347(04)00464-3
Article electronically published on August 27, 2004
THE THRESHOLD FOR RANDOM k-SAT IS 2k
log 2 - O(k)
DIMITRIS ACHLIOPTAS AND YUVAL PERES
1. Introduction
Call a disjunction of k Boolean variables a k-clause. For a set V of n Boolean
variables, let Ck(V ) denote the set of all 2k
nk
possible k-clauses on V . A random
k-CNF 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 k-CNF 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.

  

Source: Achlioptas, Dimitris - Department of Computer Engineering, University of California at Santa Cruz

 

Collections: Computer Technologies and Information Sciences