This paper focuses on the algebraic expression of discrete event systems (DES), which bridges the gap between linear control system theory and discrete event system theory. For this purpose, we firstly give an overview of different approaches towards an algebraic description existing in the literature in the area of different classes of DES, such as Petri nets, automata and Boolean networks. After that, the complexity, applicability for control and the structural restrictions are compared. Finally, possible future developments are highlighted.

中文翻译：

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离散事件系统的代数描述方法的概述和比较

本文着重研究离散事件系统（DES）的代数表达形式，它在线性控制系统理论和离散事件系统理论之间架起了桥梁。为此，我们首先概述在不同类别的DES（例如Petri网，自动机和布尔型网络）领域中对文献中存在的代数描述的不同方法。之后，比较了复杂性，控制的适用性和结构限制。最后，强调了可能的未来发展。