Algorithms for Finding Attractors of Generalized Asynchronous Random Boolean Networks

Boolean networks are considered as popular formal models for the dynamics of gene regulatory networks. There are many different types of Boolean networks, depending on their updating scheme (synchronous, asynchronous, deterministic, non-deterministic), such as Classical Random Boolean Networks (CRBNs), Asynchronous Random Boolean Networks (ARBNs), Generalized Asynchronous Random Boolean Networks (GARBNs), Deterministic Asynchronous Random Boolean Networks (DARBNs), Deterministic Generalized Asynchronous Random Boolean Networks (DGARBNs). An important long-term behavior of Boolean networks, so-called attractor, can provide valuable insights into the origins of cancer. Many studies have been done on attractors in CRBNs and ARBNs. However, in our best knowledge, there is no study on attractor detection in GARBNs, DARBNs, or DGARBNs. In this paper, we study properties of attractors in GARBNs, their relations with attractors in CRBNs, also propose different algorithms for attractor detection. Experiments are conducted on real and artificial networks to compare the performance of the proposed algorithms.