In effect, many techniques that have become standard in the study of random instances (3CNF formulas and graphs) just do not carry over to [[P.sup.sat].sub.n, m]--at least not directly.
Lemma 3 ([[P.sup.plant].sub.n, m] [right arrow] [[P.sup.sat].sub.n, m]) Let A be some property of 3CNF formulas, then
For a 3CNF formula F and a variable x we let [N.sup.+] (x) be the set of clauses in F in which x appears positively (namely, as the literal x), and [N.sup.-] (x) be the set of clauses in which x appears negatively (that is, as x).
Definition 9 (support) Given a 3CNF formula F and some assignment [psi] to the variables, we say that a literal x supports a clause C (in which it appears) w.r.t.
Trying to shed some light on this problem we consider the uniform distribution over satisfiable 3CNF formulas, [[P.sup.sat].sub.n, m], with clause-variable ratio greater than some sufficiently large constant.
Finding a randomly planted assignment in a random 3CNF. manuscript, 2002.