Analysis of Boolean Networks Using an Optimized Algorithm of Structure Matrix Based on Semi-tensor Product

The structure matrix based on semi-tensor product can provide formulas for analyzing the characteristics of a Boolean network, such as the number of fixed points, the number of circles of different lengths, transient period for all points to enter the set of attractors and basin of each attractor. However, the conventional method of semi-tensor product gains the structure matrix through complex matrix operations with high computation complexity. This paper proposes an optimized algorithm which gains the structure matrix through the truth table reflecting the state transformation of Boolean networks. The effectiveness and feasibility of our optimized approach are demonstrated through the analysis of a practical Boolean network of the mammalian cell.