SIAM Journal on Control and Optimization, Volume 59, Issue 2, Page 1033-1056, January 2021.
The concept of bisimulation has been recently introduced in the study of Boolean control networks (BCNs). The notion provides a perspective that explains how a state trajectory of one BCN can be paired with a state trajectory of another BCN, and vice versa. The present paper further pursues the notion of bisimulation in BCNs. It first gives necessary and sufficient conditions for checking this notion. The conditions are more general and neater than those previously published; more importantly, they allow us to go further to consider reducing a BCN via bisimulation. A bisimulation-based methodology is then proposed to reduce the size of the state space of a BCN. Applying the reduction methodology allows one to infer control properties of a BCN from those of the corresponding reduced system. Possibilities of applications of the results are illustrated on several Boolean models of real biomolecular systems.

中文翻译：

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通过双仿真对布尔控制网络进行约简和分析

SIAM控制与优化杂志，第59卷，第2期，第1033-1056页，2021年1月。
最近在布尔控制网络（BCN）的研究中引入了双仿真的概念。该概念提供了一个角度，该角度解释了一个BCN的状态轨迹如何与另一个BCN的状态轨迹配对，反之亦然。本文进一步探讨了BCN中的双仿真概念。首先，它为检验此概念提供了必要和充分的条件。这些条件比以前公布的条件更为笼统和整洁。更重要的是，它们使我们可以进一步考虑通过双仿真来降低BCN。然后提出了一种基于双仿真的方法，以减小BCN状态空间的大小。应用简化方法，可以从相应的简化系统的控制特性中推断出BCN的控制特性。