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10 Courses/02 - SoSe 2026/AT/29593958 - Kleene star of languages.md

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+---
+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 $L^* = {epsilon, 01, 0101, 010101, ...}$
+> $= {(01)^n bar n >= 0}$