A Study on Attractors of Generalized Asynchronous Random Boolean Networks

Boolean networks (BNs) are considered as popular formal models for the dynamics of gene regulatory networks. There are many different types of BNs, depending on their updating scheme (synchronous, asynchronous, deterministic, or 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), and Deterministic Generalized Asynchronous Random Boolean Networks (DGARBNs). An important long-term behavior of BNs, so-called attractor, can provide valuable insights into systems biology (e.g., the origins of cancer). In the previous paper [1], we have studied properties of attractors of GARBNs, their relations with attractors of CRBNs, also proposed different algorithms for attractor detection. In this paper, we propose a new algorithm based on SAT-based bounded model checking to overcome inherent problems in these algorithms. Experimental results prove the effectiveness of the new algorithm. We also show that studying attractors of GARBNs can pave potential ways to study attractors of ARBNs.