We develop a fully diagrammatic approach to finite-state automata, based on reinterpreting their usual state-transition graphical representation as a two-dimensional syntax of string diagrams. In this setting, we are able to provide a complete equational theory for language equivalence, with two notable features. First, the proposed axiomatisation is finite. Second, the Kleene star is a derived concept, as it can be decomposed into more primitive algebraic blocks.

翻译：我们提出了一种完全图解化的有限状态自动机方法，通过将其经典的状态转移图形表示重新解释为字符串图的二维语法。在此框架下，我们为语言等价性建立了一个完整的等式理论，该理论具有两个显著特征。首先，所提出的公理化体系是有限的。其次，Kleene星号是一个派生概念，因为它可以被分解为更原始的代数模块。