A Method To Study The Observability Of Conjunctive Boolean Networks

The study of genetics is difficult in the field of biology.On the one hand,the requirements need to be advanced,and on the other hand,the research results cannot be reasonably promoted.Since the key factor determining inheritance is genes,it is more valuable to build models for genes.The Boolean network quantifies the expression and non-expression of genes as numbers "1" and "0",and the relationship between genes is quantified as a Boolean function.Hence the study of the genetic inheritance can be transformed to the study of the Boolean model.The Boolean function of conjunctive Boolean networks is a special type of semilattice networks,so mathematical tools for studying semilattice networks can be used to study conjunctive Boolean networks.According to the semilattice networks,this paper defines the adjacency matrix of conjunctive Boolean networks and the multiplication of the matrix.We also introduce a new operation between the adjacency matrix and state variables of the network,which facilitates algebraization of the network.Based on the semilattice networks,this paper gives the correspondence between the composition of Boolean functions and the multiplication operation of the adjacency matrix,and proposes for determining the observability of the network.Next,this paper considers the observability of conjunctive Boolean networks with strongly connected graphs,and gives a method to judge observability of the network.The matrix used in this paper has a low order and is easy to be obtained.