vault backup: 2026-04-08 09:07:20

00 Inbox/29593852 - Strings.md

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+---
+created: 2026-04-08 08:52
+course:
+topic:
+related:
+type: lecture
+status: 🔴
+tags:
+  - university
+---
+## 📌 Summary
+
+> [!abstract]
+> 
+
+---
+
+## 📝 Content
+
+### Alphabets
+Alphabets are formal, non-empty, sets of symbols (usually lowercase letters). They are denoted by $Sigma$.
+
+$Sigma = {a, b}$
+> Alphabet $Sigma$ contains the characters $a$ and $b$.
+
+### Strings
+A string is a set of letters. If there is an alphabet $Sigma = {a,b}$ then `abba` is a string made from that alphabet.
+The empty string is denoted by $epsilon$.
+### Concatenation
+String can be concatenated, where one string is appended to another. This operation is 
+
+### Reversing / Mirroring
+For a string $x = a_1 a_2 ... a_(n-1) a_n$ of length $n$, it's _mirrored string_ is given by 
+$$ x^("Rev") = a_n a_(n-1)...a_2 a_1$$
+
+### Kleene Star
+Denoted by $Sigma^*$. The Kleene Star (or _Kleene Closure_) 
+
+### Formal Languages
+A formal _language_ of the alphabet $Sigma$ is a subset $L$ of $Sigma^*$