In this paper, we focus on the study of quotients of Boolean control networks (BCNs) with the motivation that they might serve as smaller models that still carry enough information about the original network. Given a BCN and an equivalence relation on the state set, we consider a labeled transition system that is generated by the BCN. The resulting quotient transition system then naturally captures the quotient dynamics of the BCN concerned. We therefore develop a method for constructing a Boolean system that behaves equivalently to the resulting quotient transition system. The use of the obtained quotient system for control design is discussed and we show that for BCNs, controller synthesis can be done by first designing a controller for a quotient and subsequently lifting it to the original model. We finally demonstrate the applicability of the proposed techniques on a biological example.

在本文中，我们专注于布尔控制网络（BCN）商的研究，其动机可能是它们可以用作较小的模型，并且仍然携带有关原始网络的足够信息。给定一个BCN和状态集上的等价关系，我们考虑由BCN生成的带标签的过渡系统。然后，所得的商转换系统自然地捕获了相关BCN的商动态。因此，我们开发了一种构造布尔系统的方法，该布尔系统的行为与所得商转换系统等效。讨论了所获得的商系统在控制设计中的使用，并且我们表明，对于BCN，可以通过首先为商设计控制器并将其提升到原始模型来完成控制器综合。