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Theoretical Computer Science 265 (2001) 109129 www.elsevier.com/locate/tcs

Summary: Theoretical Computer Science 265 (2001) 109­129
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,
GR-265 04 Patras, Greece
cSchool of Computer Science, Carleton University, Ottawa, Ontario, Canada K1S 5B6
In recent years there has been signi˙cant interest in the study of random k-SAT formulae. For
a given set of n Boolean variables, let Bk denote the set of all possible disjunctions of k distinct,
non-complementary literals from its variables (k-clauses). A random k-SAT 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 non-rigorous predictions on the


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


Collections: Computer Technologies and Information Sciences