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