Novel Method for Singleton and Cyclic Attractor Observability in Boolean Networks

Boolean Network (BN) is a popular and simple mathematical model which receives a lot of attention because of its capacity to reveal the behavior of a genetic regulatory network. Furthermore, observability, as a significant network feature, plays a critical role in understanding the underlying mechanism behind a genetic network. Several studies have been done on observability of BNs and complex networks. However, observability of (singleton or cyclic) attractor cycles, which can be regarded as a biomarker of disease, has not yet been fully addressed in the literature. Therefore, it becomes an urgent issue which deserves a detailed study. In this work, we first formulate a novel definition of singleton or cyclic attractor observability in BNs. Then we develop an efficient method to solve the captured problem and the complexity is of $O(P^{m}n)$, where P is the maximum period of cyclic attractor, m is the number of attractor and n is the number of genes in the network. Furthermore, we validate our model with computational experiments and show that our proposed method is effective and efficient for the captured observability problem.