Observability of Boolean networks uniquely determines an initial condition of Boolean networks with a given output sequence. The objective of this study is to simplify the observability determination of Boolean networks and to offer a strategy to reconstruct states of Boolean networks with partial states' measurement. For a given Boolean dynamics and its measurement function, we extracted implicit useful information and deleted the redundant information based on its boolean dynamics and measurement function. Then, the extracted information was transferred to an undirected graph. We derived the necessary and sufficient condition of observability determination based on the corresponding undirected graph. Such necessary and sufficient condition significantly reduced the computational cost comparing with current methods. Further, we proposed a design method to determine the measurement function and reconstruct the unmeasured states. The effectiveness of the method was illustrated with an example. In conclusion, our result established an effective tool to determine the observability for Boolean networks with arbitrary number of nodes and Boolean functions, which further provided a novel way to allocate sensors for partial state measurement and to reconstruct the entire states.
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