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Deterministic asynchronous Boolean networks play a crucial role in modeling and analysis of gene regulatory networks. In this paper, we focus on a typical type of deterministic asynchronous Boolean networks called deterministic generalized asynchronous random Boolean networks (DGARBNs). We first formulate the extended state transition graph, which captures the whole dynamics of a DGARBN and paves potential ways to analyze this DGARBN. We then propose two SMT-based methods for attractor detection and optimal control of DGARBNs. These methods are implemented in a JAVA tool called DABoolNet. Two experiments are designed to highlight the scalability of the proposed methods. We also formally state and prove several relations between DGARBNs and other models including deterministic asynchronous models, block-sequential Boolean networks, generalized asynchronous random Boolean networks, and mixed-context random Boolean networks. Several case studies are presented to show the applications of our methods. [ABSTRACT FROM AUTHOR]

Boolean networks (BNs)play a crucial role in modeling and analyzing biological systems. One of the central issues in the analysis of BNs is attractor detection, i.e., identification of all possible attractors. This problem becomes more challenging for large asynchronous random Boolean networks (ARBNs)because of the asynchronous and non-deterministic updating scheme. In this paper, we present and formally prove several relations between feedback vertex sets (FVSs)and dynamics of BNs. From these relations, we propose an FVS-based method for detecting attractors in ARBNs. Our approach relies on the principle of removing arcs in the state transition graph to get a candidate set and the reachability property to filter the candidate set. We formally prove the correctness of our method and show its efficiency by conducting experiments on real biological networks and randomly generated $N$ N - $K$ K networks. The obtained results are very promising since our method can handle large networks whose sizes are up to 101 without using any network reduction technique. [ABSTRACT FROM AUTHOR]