The exact satisfiability threshold for a potentially intractable random constraint satisfaction problem

We determine the exact threshold of satisfiability for random instances of a particular NP-hard constraint satisfaction problem. The problem appears to share many of the threshold characteristics of random k-SAT for k ≥ 3; for example, we prove the problem almost surely has high resolution complexity. We also prove the analogue of the (2+p)-SAT conjecture for a class of problems that includes this problem and XOR-SAT.