Abstract
We consider random instances of constraint satisfactionproblems where each variable has domain size O(1), eachconstraint is on O(1) variables and the constraints are chosen from a specified distribution. The number of constraints is cn where c is a constant. We prove that for every possible distribution, either the resolution complexity is almost surely polylogarithmic for sufficiently large c, or it is almost surely exponential for every c > 0. We characterize the distributions of each type. To do so, we introduce a closure operation on a set of constraints which yields the set of all constraints that, in some sense, appear implicitly in the random CSP.