Resolution Complexity of Random Constraint Satisfaction Problems: Another Half of the Story

Let C n,cn be a random constraint satisfaction problem(CSP) of n binary variables, where c > 0 is a fixed constant and the cn constraints are selected uniformly and independently from all the possible k-ary constraints each of which contains exactly t tuples of the values as its restrictions. We establish upper bounds for the tightness threshold for C n,cn to have an exponential resolution complexity. The upper bounds partly answers the open problems regarding the CSP resolution complexity with the tightness between the existing upper and lower bound [1].