 
Summary: Theoretical Computer Science 265 (2001) 109129
www.elsevier.com/locate/tcs
Rigorous results for random (2 + p)SAT
Dimitris Achlioptasa; ; 1, Lefteris M. Kirousisb, Evangelos Kranakisc,
Danny Krizancc
aMicrosoft Research, One Microsoft Way, Redmond WA 98052, USA
bDepartment of Computer Engineering and Informatics, University of Patras, University Campus,
GR265 04 Patras, Greece
cSchool of Computer Science, Carleton University, Ottawa, Ontario, Canada K1S 5B6
Abstract
In recent years there has been signi˙cant interest in the study of random kSAT formulae. For
a given set of n Boolean variables, let Bk denote the set of all possible disjunctions of k distinct,
noncomplementary literals from its variables (kclauses). A random kSAT formula Fk (n; m) is
formed by selecting uniformly and independently m clauses from Bk and taking their conjunction.
Motivated by insights from statistical mechanics that suggest a possible relationship between the
"order" of phase transitions and computational complexity, Monasson and Zecchina (Phys. Rev.
E 56(2) (1997) 1357) proposed the random (2+p)SAT model: for a given p [0; 1], a random
(2 + p)SAT formula, F2+p(n; m), has m randomly chosen clauses over n variables, where pm
clauses are chosen from B3 and (1  p)m from B2. Using the heuristic "replica method" of
statistical mechanics, Monasson and Zecchina gave a number of nonrigorous predictions on the
