Krohn-Rhodes theory encompasses the techniques for the study of finite automata and their decomposition into elementary automata. The famous result of Krohn and Rhodes roughly states that each finite automaton can be decomposed into elementary components which correspond to permutation and reset automata connected by a cascade product. However, this outcome is not easy to access for the working computer scientist. This paper provides a short introduction into Krohn-Rhodes theory based on the valuable work of Ginzburg.

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关于半自动机的 Krohn-Rhodes 理论

Krohn-Rhodes 理论包含研究有限自动机及其分解为基本自动机的技术。Krohn 和 Rhodes 的著名结果粗略地指出，每个有限自动机都可以分解为基本组件，这些基本组件对应于由级联乘积连接的置换和重置自动机。然而，对于正在工作的计算机科学家来说，这个结果并不容易获得。本文基于金茨堡的宝贵工作对 Krohn-Rhodes 理论进行了简短介绍。