Abstract This paper introduces the detectability notions and investigates the detectability properties for Boolean networks (BNs) and Boolean control networks (BCNs). A BN (BCN) possesses the property of detectability if the current state can be determined by limited observed data. According to different situations, three types of detectabilities are defined: strong detectability, detectability and weak detectability. Firstly, using the semi-tensor product of matrices, the BCN is written as an equivalent algebraic expression, which is called the data form. Secondly, some criterion and detection algorithms are provided for checking detectabilities via this novel form. Thirdly, four types of properties: stability, stabilizability, observability and detectability, are compared and analyzed, and then their relationships are clearly described in two diagrams, which provide a new perspective to analyze the characterization of BNs and BCNs. Finally, for better presentation, two practical examples are presented to show the effectiveness of the obtained new results.

中文翻译：

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关于布尔控制网络的可检测性

摘要 本文介绍了可检测性概念，并研究了布尔网络 (BN) 和布尔控制网络 (BCN) 的可检测性属性。如果当前状态可以通过有限的观察数据确定，则 BN (BCN) 具有可检测性。根据不同的情况，定义了三种可探测性：强可探测性、可探测性和弱可探测性。首先，利用矩阵的半张量积，将BCN写成等价的代数表达式，称为数据形式。其次，通过这种新颖的形式提供了一些标准和检测算法来检查可检测性。第三，对稳定性、稳定性、可观察性和可检测性四种性质进行比较和分析，然后在两张图中清楚地描述了它们的关系，这为分析 BN 和 BCN 的表征提供了一个新的视角。最后，为了更好地展示，给出了两个实际例子来展示所获得的新结果的有效性。