Matrix approach to simplify Boolean networks

The state space of Boolean networks grows exponentially with the number of nodes; this makes it hard to analyze large-scale Boolean networks. This paper aims to simplify Boolean networks mathematically by aid of a new matrix analysis tool, called semi-tensor product of matrices proposed in recent years. The simplification method contains two steps. First, delete the gene nodes that their dynamics are independent on their evolutions directly. Second, use the logic functions of the deleted nodes to replace the corresponding variables in the logic functions of other gene nodes that their dynamics are depend on themselves directly and the deleted nodes in the step 1. We prove that the reduced networks share some common key dynamics with the original networks such as the steady states, attractors and topological structure.