---
created: 2026-04-08 10:38
course: "[[29593850 - Automationtheory]]"
topic: kleene
related: "[[29593940 - Formal Languages]]"
type: lecture
status: 🟢
tags:
  - university
---
## 📌 Summary

> [!abstract]
> 

---

## 📝 Content

The _Kleene star_ $L^*$ of a language $L subset Sigma^*$ is the set of all strings (including the empty string $epsilon$) that can be generated by arbitrary concatenation of strings in the language, that is
> $L^* := union.big_(n >= 0) L^n$

> [!EXAMPLE]
> For $L = {01}$ one has $L^* = {epsilon, 01, 0101, 010101, ...}$
> $= {(01)^n bar n >= 0}$