---
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 $Sigma^*$