Phase transition in a random NK landscape model

An analysis for the phase transition in a random NK landscape model is given. For the fixed ratio model, NK(n, k, z), Gao and Culberson [17] showed that a random instance generated by NK(n, 2, z) with z > z(0) = 27-7 root 5/4 is asymptotically insoluble. Based on empirical results, they conjectured that the phase transition occurs around the value z = z(0). We prove that an instance generated by NK(n, 2, z) with z < z(0) is soluble with positive probability by providing a variant of the unit clause algorithm. Using branching process arguments, we also reprove that an instance generated by NK(n, 2, z) with z > z(0) is asymptotically insoluble. The results show the phase transition around z = z(0) for NK(n, 2, z). In the course of the analysis, we introduce a generalized random 2-SAT formula, which is of self interest, and show its phase transition phenomenon.