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vault backup: 2026-04-08 13:00:12

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Jan Meyer
2026-04-08 13:00:12 +02:00
parent d21c72e4e7
commit 8bcf049ced
4 changed files with 135 additions and 92 deletions
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164
.obsidian/snippets/matugen.css vendored
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@@ -6,113 +6,113 @@
.theme-dark, .theme-light { .theme-dark, .theme-light {
/* ── Material You RGB helpers ──────────────────────────── */ /* ── Material You RGB helpers ──────────────────────────── */
--mat-bg-rgb: 32, 14, 14; --mat-bg-rgb: 19, 18, 29;
--mat-surface-rgb: 32, 14, 14; --mat-surface-rgb: 19, 18, 29;
--mat-on-surface-rgb: 254, 218, 217; --mat-on-surface-rgb: 228, 224, 240;
--mat-primary-rgb: 255, 179, 178; --mat-primary-rgb: 195, 192, 255;
--mat-on-primary-rgb: 104, 0, 19; --mat-on-primary-rgb: 29, 0, 165;
/* ── Core Backgrounds ──────────────────────────────────── */ /* ── Core Backgrounds ──────────────────────────────────── */
--background-primary: #200e0e; --background-primary: #13121d;
--background-primary-alt: #200e0e; --background-primary-alt: #13121d;
--background-secondary: #291616; --background-secondary: #1b1a25;
--background-secondary-alt: #2e1a1a; --background-secondary-alt: #1f1e29;
/* ── Titlebar ──────────────────────────────────────────── */ /* ── Titlebar ──────────────────────────────────────────── */
--titlebar-background: #200e0e; --titlebar-background: #13121d;
--titlebar-background-focused: #291616; --titlebar-background-focused: #1b1a25;
--titlebar-text-color: #fedad9; --titlebar-text-color: #e4e0f0;
/* ── Borders & Dividers ────────────────────────────────── */ /* ── Borders & Dividers ────────────────────────────────── */
--background-modifier-border: #5e3f3e; --background-modifier-border: #464557;
--background-modifier-border-focus: #ae8786; --background-modifier-border-focus: #918fa3;
--background-modifier-border-hover: #ae8786; --background-modifier-border-hover: #918fa3;
/* ── Text Colors ───────────────────────────────────────── */ /* ── Text Colors ───────────────────────────────────────── */
--text-normal: #fedad9; --text-normal: #e4e0f0;
--text-muted: #e8bcbb; --text-muted: #c7c4da;
--text-faint: #ae8786; --text-faint: #918fa3;
--text-on-accent: #680013; --text-on-accent: #1d00a5;
--text-selection: rgba(255, 179, 178, 0.25); --text-selection: rgba(195, 192, 255, 0.25);
/* ── Accent & Interactive ──────────────────────────────── */ /* ── Accent & Interactive ──────────────────────────────── */
--interactive-accent: #ffb3b2; --interactive-accent: #c3c0ff;
--interactive-accent-hover: #ff525d; --interactive-accent-hover: #3c24f6;
--interactive-accent-rgb: 255, 179, 178; --interactive-accent-rgb: 195, 192, 255;
--text-accent: #ffb3b2; --text-accent: #c3c0ff;
--text-accent-hover: #ff525d; --text-accent-hover: #3c24f6;
/* ── Hover & Active Modifiers ──────────────────────────── */ /* ── Hover & Active Modifiers ──────────────────────────── */
--background-modifier-hover: rgba(var(--mat-on-surface-rgb), 0.06); --background-modifier-hover: rgba(var(--mat-on-surface-rgb), 0.06);
--background-modifier-active-hover: rgba(var(--mat-primary-rgb), 0.15); --background-modifier-active-hover: rgba(var(--mat-primary-rgb), 0.15);
--background-modifier-success: #2f9fa4; --background-modifier-success: #a32200;
--background-modifier-error: #93000a; --background-modifier-error: #93000a;
--background-modifier-error-hover: #ffb4ab; --background-modifier-error-hover: #ffb4ab;
/* ── Obsidian Color Scale (--color-base-XX) ────────────── */ /* ── Obsidian Color Scale (--color-base-XX) ────────────── */
--color-base-00: #200e0e; --color-base-00: #13121d;
--color-base-05: #200e0e; --color-base-05: #13121d;
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--color-base-20: #291616; --color-base-20: #1b1a25;
--color-base-25: #2e1a1a; --color-base-25: #1f1e29;
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--color-base-35: #452f2f; --color-base-35: #34343f;
--color-base-40: #5e3f3e; --color-base-40: #464557;
--color-base-50: #ae8786; --color-base-50: #918fa3;
--color-base-60: #e8bcbb; --color-base-60: #c7c4da;
--color-base-70: #fedad9; --color-base-70: #e4e0f0;
--color-base-100: #fedad9; --color-base-100: #e4e0f0;
/* ── Semantic Colors ───────────────────────────────────── */ /* ── Semantic Colors ───────────────────────────────────── */
--color-red: #ffb4ab; --color-red: #ffb4ab;
--color-orange: #70d6db; --color-orange: #ffb4a3;
--color-yellow: #ffb3b2; --color-yellow: #c3c0ff;
--color-green: #2f9fa4; --color-green: #a32200;
--color-cyan: #8f0d21; --color-cyan: #3e3a96;
--color-blue: #ffb3b2; --color-blue: #c3c0ff;
--color-purple: #ffb3b2; --color-purple: #c3c0ff;
--color-pink: #70d6db; --color-pink: #ffb4a3;
/* ── Headings ──────────────────────────────────────────── */ /* ── Headings ──────────────────────────────────────────── */
--h1-color: #ffb3b2; --h1-color: #c3c0ff;
--h2-color: #ffb3b2; --h2-color: #c3c0ff;
--h3-color: #ffb3b2; --h3-color: #c3c0ff;
--h4-color: #70d6db; --h4-color: #ffb4a3;
--h5-color: #e8bcbb; --h5-color: #c7c4da;
--h6-color: #ae8786; --h6-color: #918fa3;
/* ── Links ─────────────────────────────────────────────── */ /* ── Links ─────────────────────────────────────────────── */
--link-color: #ffb3b2; --link-color: #c3c0ff;
--link-color-hover: #000000; --link-color-hover: #faf6ff;
--link-external-color: #70d6db; --link-external-color: #ffb4a3;
--link-unresolved-color: #ae8786; --link-unresolved-color: #918fa3;
/* ── Tags ──────────────────────────────────────────────── */ /* ── Tags ──────────────────────────────────────────────── */
--tag-color: #000000; --tag-color: #faf6ff;
--tag-background: #ff525d; --tag-background: #3c24f6;
--tag-border-color: #ffb3b2; --tag-border-color: #c3c0ff;
--tag-color-hover: #680013; --tag-color-hover: #1d00a5;
--tag-background-hover: #ffb3b2; --tag-background-hover: #c3c0ff;
/* ── Checkboxes ────────────────────────────────────────── */ /* ── Checkboxes ────────────────────────────────────────── */
--checkbox-color: #ffb3b2; --checkbox-color: #c3c0ff;
--checkbox-color-hover: #ff525d; --checkbox-color-hover: #3c24f6;
--checkbox-border-color: #ae8786; --checkbox-border-color: #918fa3;
--checkbox-marker-color: #680013; --checkbox-marker-color: #1d00a5;
/* ── Code Blocks ───────────────────────────────────────── */ /* ── Code Blocks ───────────────────────────────────────── */
--code-background: #291616; --code-background: #1b1a25;
--code-normal: #fedad9; --code-normal: #e4e0f0;
--code-comment: #ae8786; --code-comment: #918fa3;
--code-function: #ffb3b2; --code-function: #c3c0ff;
--code-important: #ffb4ab; --code-important: #ffb4ab;
--code-keyword: #ffb3b2; --code-keyword: #c3c0ff;
--code-operator: #70d6db; --code-operator: #ffb4a3;
--code-property: #e8bcbb; --code-property: #c7c4da;
--code-punctuation: #5e3f3e; --code-punctuation: #464557;
--code-string: #70d6db; --code-string: #ffb4a3;
--code-tag: #ffb4ab; --code-tag: #ffb4ab;
--code-value: #ffb3b2; --code-value: #c3c0ff;
/* ── Scrollbar ─────────────────────────────────────────── */ /* ── Scrollbar ─────────────────────────────────────────── */
--scrollbar-thumb-bg: rgba(var(--mat-on-surface-rgb), 0.12); --scrollbar-thumb-bg: rgba(var(--mat-on-surface-rgb), 0.12);
@@ -121,16 +121,16 @@
/* ── Inputs ────────────────────────────────────────────── */ /* ── Inputs ────────────────────────────────────────────── */
--input-shadow: none; --input-shadow: none;
--input-shadow-hover: 0 0 0 2px #ae8786; --input-shadow-hover: 0 0 0 2px #918fa3;
/* ── Graph View ────────────────────────────────────────── */ /* ── Graph View ────────────────────────────────────────── */
--graph-node: #ffb3b2; --graph-node: #c3c0ff;
--graph-node-unresolved: #ae8786; --graph-node-unresolved: #918fa3;
--graph-node-focused: #000000; --graph-node-focused: #faf6ff;
--graph-node-tag: #ffb3b2; --graph-node-tag: #c3c0ff;
--graph-node-attachment: #70d6db; --graph-node-attachment: #ffb4a3;
--graph-line: #5e3f3e; --graph-line: #464557;
--graph-background: #200e0e; --graph-background: #13121d;
} }

26
.obsidian/workspace.json vendored
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@@ -20,8 +20,23 @@
"icon": "lucide-file", "icon": "lucide-file",
"title": "29593852 - Strings" "title": "29593852 - Strings"
} }
},
{
"id": "e179fd2c20f4067e",
"type": "leaf",
"state": {
"type": "markdown",
"state": {
"file": "00 Inbox/29593975 - Regular Expressions.md",
"mode": "source",
"source": false
},
"icon": "lucide-file",
"title": "29593975 - Regular Expressions"
} }
] }
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@@ -78,7 +93,7 @@
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@@ -182,16 +197,17 @@
"darlal-switcher-plus:Open Symbols for the active editor": false "darlal-switcher-plus:Open Symbols for the active editor": false
} }
}, },
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"10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593952 - Regular Languages.md", "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/29593852 - Strings.md",
"10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593952 - Regular Languages.md",
"10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593958 - Kleene star of languages.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/29593962 - atfl-st2026-l02-finite-representation-of-languages-full.pdf",
"30 Library/normalize_name.sh", "30 Library/normalize_name.sh",
"30 Library/atfl-st2026-l02-finite-representation-of-languages-full.pdf", "30 Library/atfl-st2026-l02-finite-representation-of-languages-full.pdf",
"10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593935 - Kleene.md", "10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593935 - Kleene.md",
"10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593940 - Formal Languages.md",
"30 Library/29593895 - atfl-st2026-l01-formal-languages-full.pdf", "30 Library/29593895 - atfl-st2026-l01-formal-languages-full.pdf",
"10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593929 - Alphabets.md", "10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593929 - Alphabets.md",
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31
00 Inbox/29593975 - Regular Expressions.md Normal file
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@@ -0,0 +1,31 @@
---
created: 2026-04-08 10:55
course: "[[29593850 - Automationtheory]]"
topic: languages
related: "[[29593940 - Formal Languages#Finite representation of languages]]"
type: lecture
status: 🔴
tags:
- university
---
## 📌 Summary
> [!abstract]
>
---
## 📝 Content
A _regular expression_ $r$ over an alphabet $Sigma$ is defined recursively:
- $emptyset, epsilon$ and each $a in Sigma$ are regular expression, which represent the Languages $L(emptyset) = emptyset, L(epsilon) = {epsilon}$ and $L(a) = {a}$
- If $r$ and $s$ are regular expressions then these are also regular expressions:
- $(r + s)$ with $L(r + s) = L(r) union L(s)$
- $(r s)$ with $L(r s) = L(r)L(s)$
- $r^*$ with $L(r^*) = L(r)^*$
> [!EXAMPLE]
> The language $L$ over $Sigma = {a, b}$ containing the substring $a b$ is regular, since it can be expressed using the regular expression
> $r = (a +b)^* a b (a + b)^*$

6
10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593940 - Formal Languages.md
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@@ -49,10 +49,6 @@ The $n^"th"$ power of the language $L subset.eq Sigma^*$ over alphabet $Sigma$
**Goal:** Represent a language using _finite_ information **Goal:** Represent a language using _finite_ information
### Using set notation ### Using set notation
$S = {a^n b^m bar n, m >= 0} = {epsilon, a, b, "aa", "ab", ...}$ $S = {a^n b^m bar n, m >= 0} = {epsilon, a, b, "aa", "ab", ...}$
> This is very inefficient. > This is limited in practice.
### Using regular expressions ### Using regular expressions
A _regular expression_ $r$ over an alphabet $Sigma$ is defined recursively:
- $emptyset, epsilon$ and each $a in Sigma$ are regular expression, which represent the Languages $L(emptyset) = emptyset, L(epsilon) = {epsilon}$ and $L(a) = {a}$
- If $r$ and $s$ are regular expressions then
- $(r+s)$