Abstract | In recent years there has been signi1cant 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 selectinguniformly and independently m clauses from Bk and takingtheir 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. Usingthe heuristic ?replica method? of
statistical mechanics, Monasson and Zecchina gave a number of non-rigorous predictions on the
behavior of random (2 + p)-SAT formulae. In this paper we give the 1rst rigorous results for
random (2 + p)-SAT, includingthe followingsurprisingfact: for p 6 2=5, with probability
1 − o(1), a random (2 + p)-SAT formula is satis1able i@ its 2-SAT subformula is satis1able.
That is, for p 6 2=5, random (2 + p)-SAT behaves like random 2-SAT. |