Author(s)

Ya'nan Liu

College of Science, University of Shanghai for Science and Technology, Shanghai, China.

The phenomenon of phase transition in constraint satisfaction problems (CSPs) plays a crucial role in the field of artificial intelligence and computational complexity theory. In this paper, we propose a new random CSP called d-p-RB model, which is a generalization of RB model on domain size d and constraint tightness p. In this model, the variable domain size d Ε [ n^α, n^ny], and all constraints are uniformly divided into several groups with different constraint tightness p. It is proved by the second moment method that the d-p-RB model undergoes phase transition from a region where almost all instances are satisfiable to a region where almost all instances are unsatisfiable as the control parameter increases. Moreover, the threshold value at which the phase transition occurs is located exactly.

d-p-RB Model, Phase Transition, Domain Size, Constraint Tightness, Second Moment Method

Liu, Y. (2017) Sharp Thresholds for a Random Constraint Satisfaction Problem. Open Journal of Applied Sciences, 7, 574-584. doi: 10.4236/ojapps.2017.710041.