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10 Courses/02 - SoSe 2026/AT/29593935 - Kleene Star & Kleene Plus.md

@@ -11,14 +11,15 @@ tags:
 ## 📌 Summary
 
 > [!abstract]
-> 
+> Definition and Examples of the Kleene Star, the Kleene Plus and the Lemma Group Structure
+ 
 
 ---
 
 ## 📝 Content
 
 ### Kleene Star
-Denoted by $Sigma^*$. The Kleene Star (or _Kleene operator_ or _Kleene Closure_) gives an infinite amount of strings made up of the characters of the alphabet $Sigma ^ *$. 
+Denoted by $Sigma^*$. The Kleene Star (or _Kleene operator_ or _Kleene Closure_) gives an infinite amount of [[29593852 - Strings|strings]] made up of the characters of the [[29593929 - Alphabets|alphabets]] $Sigma ^ *$. 
 $Sigma^*$ is the set of all string that can be generated by arbitrary concatenation of its characters.
 > $Sigma^* := union.big_(n>=0) A_n$
 > where $A_n$ is the set of all string combinations of length $n$
@@ -38,7 +39,7 @@ $Sigma^*$ is the set of all string that can be generated by arbitrary concatenat
 The _Kleene Plus_ of an alphabet $Sigma$ is given by $Sigma^+ = Sigma^* backslash {epsilon}$ 
 
 ### Lemma group structure
-The structure _Lemma_ is induced by the Kleene star - it is a monoid, that is a semigroup with a neutral element.
+The _Lemma group structure_ is induced by the [[29593935 - Kleene Star & Kleene Plus#Kleene Star|Kleene Star]] - it is a monoid, that is a semigroup with a neutral element.
 
 > [!PROOF]
 > - Associativity has been shown