From 33843cd0e6c4f4d4f90b1a5ca6b9ed584e142264 Mon Sep 17 00:00:00 2001 From: Jan Meyer Date: Wed, 8 Apr 2026 15:10:32 +0200 Subject: [PATCH] vault backup: 2026-04-08 15:10:32 --- .obsidian/workspace.json | 20 ++++++++++++++++--- 00 Inbox/29593975 - Regular Expressions.md | 4 +++- .../29593952 - Regular Languages.md | 6 +++++- 3 files changed, 25 insertions(+), 5 deletions(-) diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json index 309e96b..3002a9d 100644 --- a/.obsidian/workspace.json +++ b/.obsidian/workspace.json @@ -34,6 +34,20 @@ "icon": "lucide-file", "title": "29593975 - Regular Expressions" } + }, + { + "id": "1e58a188bb5d367b", + "type": "leaf", + "state": { + "type": "markdown", + "state": { + "file": "10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593952 - Regular Languages.md", + "mode": "source", + "source": false + }, + "icon": "lucide-file", + "title": "29593952 - Regular Languages" + } } ], "currentTab": 1 @@ -199,10 +213,10 @@ }, "active": "e179fd2c20f4067e", "lastOpenFiles": [ - "10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593940 - Formal Languages.md", - "00 Inbox/29593975 - Regular Expressions.md", - "10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593852 - Strings.md", "10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593952 - Regular Languages.md", + "00 Inbox/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", "30 Library/29593962 - atfl-st2026-l02-finite-representation-of-languages-full.pdf", "30 Library/normalize_name.sh", diff --git a/00 Inbox/29593975 - Regular Expressions.md b/00 Inbox/29593975 - Regular Expressions.md index cb4c408..b405d3c 100644 --- a/00 Inbox/29593975 - Regular Expressions.md +++ b/00 Inbox/29593975 - Regular Expressions.md @@ -28,4 +28,6 @@ A _regular expression_ $r$ over an alphabet $Sigma$ is defined recursively: > [!EXAMPLE] > The language $L$ over $Sigma = {a, b}$ containing the substring $a b$ is regular, since it can be expressed using the regular expression > $r = (a +b)^* a b (a + b)^*$ - \ No newline at end of file + +## Equivalence of regular expressions +Two regular expressiosn $r$ and $s$ are _equivalent_ ($r eq.triple s$ or $r hat(eq) s$) if thy generate the same language ($L(r) eq L(s)$). \ No newline at end of file diff --git a/10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593952 - Regular Languages.md b/10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593952 - Regular Languages.md index bf4338d..1036414 100644 --- a/10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593952 - Regular Languages.md +++ b/10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593952 - Regular Languages.md @@ -17,4 +17,8 @@ tags: ## 📝 Content -A language $L$ that can be described by a regular expression $r$ (i. e. $L(r) = L$) is called _regular_. \ No newline at end of file +A language $L$ that can be described by a [[29593975 - Regular Expressions|Regular Expression]] $r$ (i. e. $L(r) = L$) is called _regular_. + +> [!WARNING] +> There a several important languages that **cannot** be described by a regular expression. +> (proof later)