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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 me