diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json index 3a2e601..3b1b787 100644 --- a/.obsidian/workspace.json +++ b/.obsidian/workspace.json @@ -13,7 +13,7 @@ "state": { "type": "markdown", "state": { - "file": "10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593852 - Strings.md", + "file": "10 Courses/02 - SoSe 2026/AT/29593852 - Strings.md", "mode": "source", "source": false }, @@ -27,12 +27,12 @@ "state": { "type": "markdown", "state": { - "file": "10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593975 - Regular Expressions.md", + "file": "10 Courses/02 - SoSe 2026/AT/29593850 - Automationtheory.md", "mode": "source", "source": false }, "icon": "lucide-file", - "title": "29593975 - Regular Expressions" + "title": "29593850 - Automationtheory" } }, { @@ -41,7 +41,7 @@ "state": { "type": "markdown", "state": { - "file": "10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593952 - Regular Languages.md", + "file": "10 Courses/02 - SoSe 2026/AT/29593952 - Regular Languages.md", "mode": "source", "source": false }, @@ -211,25 +211,27 @@ "darlal-switcher-plus:Open Symbols for the active editor": false } }, - "active": "7a0e7b37bd89861d", + "active": "e179fd2c20f4067e", "lastOpenFiles": [ - "10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593952 - Regular Languages.md", - "10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593975 - Regular Expressions.md", - "10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593940 - Formal Languages.md", - "10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593852 - Strings.md", - "10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593958 - Kleene star of languages.md", + "99 Templates/New File Template.md", + "10 Courses/02 - SoSe 2026/AT/29593940 - Formal Languages.md", + "10 Courses/02 - SoSe 2026/AT/29593935 - Kleene Star & Kleene Plus.md", + "10 Courses/02 - SoSe 2026/AT/29593958 - Kleene star of languages.md", + "20 Atlas/AT - Map of Content.md", + "20 Atlas/ET II - Map of Content.md", + "10 Courses/02 - SoSe 2026/AT/29593929 - Alphabets.md", + "10 Courses/02 - SoSe 2026/AT/29593852 - Strings.md", + "10 Courses/02 - SoSe 2026/AT/29593850 - Automationtheory.md", + "10 Courses/02 - SoSe 2026/AT/29593975 - Regular Expressions.md", + "10 Courses/02 - SoSe 2026/AT/29593952 - Regular Languages.md", "30 Library/29593962 - atfl-st2026-l02-finite-representation-of-languages-full.pdf", "30 Library/normalize_name.sh", "30 Library/atfl-st2026-l02-finite-representation-of-languages-full.pdf", - "10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593935 - Kleene.md", "30 Library/29593895 - atfl-st2026-l01-formal-languages-full.pdf", - "10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593929 - Alphabets.md", "30 Library/29592593 - ET_II_Folien_gesamt_020426.pdf", "30 Library/29592593 - 29592593 - ET_II_Folien_gesamt_020426.pdf", "30 Library/atfl-st2026-l01-formal-languages-full.pdf", - "10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593850 - Automationtheory.md", "10 Courses/02 - SoSe 2026/ET II/29592673 - Elektrotechnik II.md", - "99 Templates/New File Template.md", "99 Templates/New File Template.md~", "00 Inbox/29593849 - Automationtheory.md", "00 Inbox/29593844 - Basics of formal languages.md", @@ -241,13 +243,11 @@ "00 Inbox/newfile.md", "00 Inbox/29593832 - 2026-04-08.md", "10 Courses/02 - SoSe 2026/ET II/29592733 - Zählpfeilsysteme.md", - "10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen", + "10 Courses/02 - SoSe 2026/AT", "10 Courses/02 - SoSe 2026/ET II/29592751 - Übungsaufgabe 1.md", "10 Courses/02 - SoSe 2026/ET II/29592755 - Übungsaufgabe 2.md", - "20 Atlas/ET II - Map of Content.md", "00 Inbox/29593226 - ET_II_Folien_gesamt_020426.pdf.md", "10 Courses/02 - SoSe 2026/ET II/29592722 - Zeitabhängige Größen.md", - "10 Courses/02 - SoSe 2026/ET II/29592709 - Klausur.md", "20 Atlas", "10 Courses/01 - WiSe 2025_26/ET/images/beispiel_knotenregel.png" ] diff --git a/10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593850 - Automationtheory.md b/10 Courses/02 - SoSe 2026/AT/29593850 - Automationtheory.md similarity index 100% rename from 10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593850 - Automationtheory.md rename to 10 Courses/02 - SoSe 2026/AT/29593850 - Automationtheory.md diff --git a/10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593852 - Strings.md b/10 Courses/02 - SoSe 2026/AT/29593852 - Strings.md similarity index 100% rename from 10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593852 - Strings.md rename to 10 Courses/02 - SoSe 2026/AT/29593852 - Strings.md diff --git a/10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593929 - Alphabets.md b/10 Courses/02 - SoSe 2026/AT/29593929 - Alphabets.md similarity index 100% rename from 10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593929 - Alphabets.md rename to 10 Courses/02 - SoSe 2026/AT/29593929 - Alphabets.md diff --git a/10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593935 - Kleene.md b/10 Courses/02 - SoSe 2026/AT/29593935 - Kleene Star & Kleene Plus.md similarity index 75% rename from 10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593935 - Kleene.md rename to 10 Courses/02 - SoSe 2026/AT/29593935 - Kleene Star & Kleene Plus.md index 04dcdb0..ae94d62 100644 --- a/10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593935 - Kleene.md +++ b/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 diff --git a/10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593940 - Formal Languages.md b/10 Courses/02 - SoSe 2026/AT/29593940 - Formal Languages.md similarity index 100% rename from 10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593940 - Formal Languages.md rename to 10 Courses/02 - SoSe 2026/AT/29593940 - Formal Languages.md diff --git a/10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593952 - Regular Languages.md b/10 Courses/02 - SoSe 2026/AT/29593952 - Regular Languages.md similarity index 100% rename from 10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593952 - Regular Languages.md rename to 10 Courses/02 - SoSe 2026/AT/29593952 - Regular Languages.md diff --git a/10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593958 - Kleene star of languages.md b/10 Courses/02 - SoSe 2026/AT/29593958 - Kleene star of languages.md similarity index 100% rename from 10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593958 - Kleene star of languages.md rename to 10 Courses/02 - SoSe 2026/AT/29593958 - Kleene star of languages.md diff --git a/10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593975 - Regular Expressions.md b/10 Courses/02 - SoSe 2026/AT/29593975 - Regular Expressions.md similarity index 100% rename from 10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593975 - Regular Expressions.md rename to 10 Courses/02 - SoSe 2026/AT/29593975 - Regular Expressions.md diff --git a/20 Atlas/AT - Map of Content.md b/20 Atlas/AT - Map of Content.md new file mode 100644 index 0000000..1cbb950 --- /dev/null +++ b/20 Atlas/AT - Map of Content.md @@ -0,0 +1,6 @@ +```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 +```