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Jan Meyer
2026-04-08 15:10:32 +02:00
parent 8bcf049ced
commit 33843cd0e6
3 changed files with 25 additions and 5 deletions
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.obsidian/workspace.json vendored
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@@ -34,6 +34,20 @@
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"title": "29593975 - Regular Expressions" "title": "29593975 - Regular Expressions"
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00 Inbox/29593975 - Regular Expressions.md
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@@ -28,4 +28,6 @@ A _regular expression_ $r$ over an alphabet $Sigma$ is defined recursively:
> [!EXAMPLE] > [!EXAMPLE]
> The language $L$ over $Sigma = {a, b}$ containing the substring $a b$ is regular, since it can be expressed using the regular expression > The language $L$ over $Sigma = {a, b}$ containing the substring $a b$ is regular, since it can be expressed using the regular expression
> $r = (a +b)^* a b (a + b)^*$ > $r = (a +b)^* a b (a + b)^*$
## 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 ($L(r) eq L(s)$).

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10 Courses/02 - SoSe 2026/Automatentheorie und formale Sprachen/29593952 - Regular Languages.md
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@@ -17,4 +17,8 @@ tags:
## 📝 Content ## 📝 Content
A language $L$ that can be described by a regular expression $r$ (i. e. $L(r) = L$) is called _regular_. 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.
> <mark style="background: #CACFD9A6;">(proof later)</mark>