REVERSE ENGINEERING OF THE NK BOOLEAN NETWORK AND ITS EXTENSION — FUZZY LOGIC NETWORK

In this paper, we first propose a reverse engineering solution to decode the NK Boolean dynamic network given the input and output of the system. This theory utilizes basis functions and dynamic matrices, through which the network's evolutionary behavior can be simulated in a rigorous mathematical manner. Then, a general network model, fuzzy logic network (FLN), is presented as the extension of the Boolean network. This novel network model assigns variable values in a continuous domain, and it can accommodate internal conflicts among variables. In addition, the FLN uses fuzzy logical functions instead of Boolean logical functions, which enables it to model highly non-linear relationships and periodicity. Using the approach of annealed approximations, we proved important theorems concerning the dynamic property of the FLN. Combined with the Zipf's law, the criteria of applying FLN to the modeling of gene regulatory networks were achieved.