Resolution complexity of random constraint satisfaction problems: Another half of the story

Let Cn,m2,k,t be a random constraint satisfaction problem (CSP) on n binary variables, where m constraints are selected uniformly at random from all the possible k-ary constraints each of which contains exactly t tuples of the values as its restrictions. We establish an upper bound on the constraint tightness threshold for Cn,m2,k,t to have an exponential resolution complexity. The upper bound partly answers the open problem regarding the CSP resolution complexity with the tightness between the existing upper and lower bounds [D. Mitchell, Resolution complexity of random constraints, in: Proceedings Principles and Practices of Constraint Programming-CP 2002, Springer, Berlin, 2002, pp. 295-309].