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Jan Meyer
2026-04-08 17:42:58 +02:00
parent 518f51dd42
commit 94aa5c9951
10 changed files with 27 additions and 20 deletions
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34
.obsidian/workspace.json vendored
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@@ -13,7 +13,7 @@
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@@ -27,12 +27,12 @@
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@@ -41,7 +41,7 @@
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"mode": "source", "mode": "source",
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}, },
@@ -211,25 +211,27 @@
"darlal-switcher-plus:Open Symbols for the active editor": false "darlal-switcher-plus:Open Symbols for the active editor": false
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0
10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593850 - Automationtheory.md → 10 Courses/02 - SoSe 2026/AT/29593850 - Automationtheory.md
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0
10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593852 - Strings.md → 10 Courses/02 - SoSe 2026/AT/29593852 - Strings.md
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0
10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593929 - Alphabets.md → 10 Courses/02 - SoSe 2026/AT/29593929 - Alphabets.md
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7
10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593935 - Kleene.md → 10 Courses/02 - SoSe 2026/AT/29593935 - Kleene Star & Kleene Plus.md
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@@ -11,14 +11,15 @@ tags:
## 📌 Summary ## 📌 Summary
> [!abstract] > [!abstract]
> > Definition and Examples of the Kleene Star, the Kleene Plus and the Lemma Group Structure
--- ---
## 📝 Content ## 📝 Content
### Kleene Star ### 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. $Sigma^*$ is the set of all string that can be generated by arbitrary concatenation of its characters.
> $Sigma^* := union.big_(n>=0) A_n$ > $Sigma^* := union.big_(n>=0) A_n$
> where $A_n$ is the set of all string combinations of length $n$ > 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 $Sigma^+ = Sigma^* backslash {epsilon}$ The _Kleene Plus_ of an alphabet $Sigma$ is given by $Sigma^+ = Sigma^* backslash {epsilon}$
### Lemma group structure ### 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] > [!PROOF]
> - Associativity has been shown > - Associativity has been shown

0
10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593940 - Formal Languages.md → 10 Courses/02 - SoSe 2026/AT/29593940 - Formal Languages.md
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0
10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593952 - Regular Languages.md → 10 Courses/02 - SoSe 2026/AT/29593952 - Regular Languages.md
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0
10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593958 - Kleene star of languages.md → 10 Courses/02 - SoSe 2026/AT/29593958 - Kleene star of languages.md
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0
10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593975 - Regular Expressions.md → 10 Courses/02 - SoSe 2026/AT/29593975 - Regular Expressions.md
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6
20 Atlas/AT - Map of Content.md Normal file
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```dataview
TABLE topic AS "Concept", status AS "Review Status"
FROM "10 Courses/02 - SoSe 2026/AT"
WHERE type = "lecture" OR type = "concept"
SORT created ASC
```