On Krohn-Rhodes theory for semiautomata

TL;DR

This paper introduces Krohn-Rhodes theory, explaining how finite automata can be decomposed into elementary components, making the complex theory more accessible to computer scientists.

Contribution

It provides an accessible introduction to Krohn-Rhodes theory, highlighting its decomposition techniques based on Ginzburg's work.

Findings

Decomposition of finite automata into elementary automata

Connection between permutation and reset automata

Cascade product structure of automata

Abstract

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.