An Improved Method for Finding Attractors of Large-Scale Asynchronous Boolean Networks

Attractor detection in Asynchronous Boolean Networks (ABNs) is very challenging due to the high complexity of the state transition graph of an ABN. Recently, an efficient method (called FVS-ARBN) has been proposed for exactly finding attractors of an ABN. FVS-ARBN uses a Feedback Vertex Set (FVS) to get a candidate set of states, then filters out this set by checking the reachability in ABNs. This method gives promising results; however, it still needs to be improved to handle larger networks. In this paper, we propose a new method (named iFVS-ABN) that includes two improvements to FVS-ARBN. First, we propose a reasonable combination of multiple existing techniques to efficiently check the reachability in ABNs. Second, we formally state and prove a relation between a Negative Feedback Vertex Set (NFVS) and the dynamics of an ABN. Based on this relation, we propose to use an NFVS instead of an FVS to get the candidate set of states. Experimental results show that the two improvements are effective and the improved method outperforms the original one.