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This technical note presents analytical investigations of reachability and controllability of Boolean control networks (BCNs) with pinning controllers. Based on semi-tensor product (STP) of matrices, BCNs with pinning controllers are converted into a discrete-time algebraic system. A formula is derived to calculate the number of different control sequences steering BCNs between two states in a given step, and then several necessary and sufficient criteria are derived for reachability and controllability of BCNs with pinning controllers. Moreover, we make a comparison among three forms of BCNs, which have similar algebraic representations. Finally, we obtain some efficient conditions to judge the dynamic structure of BCNs.
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Lu et al. (2015) studied this question.
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