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An alphabet $\Sigma$ is a nonempty finite set such that every string formed by elements of $\Sigma$ can be decomposed uniquely into elements of $\Sigma$.
For example, $\{b,lo,g,bl,og\}$ is not a valid alphabet because the string $blog$ can be broken up in two ways: b lo g and bl og. $\{\mathbb{C}a,\ddot{n}a,{\rm d},a\}$ is a valid alphabet, because there is only one way to fully break up any given string formed from it.
If $\Sigma$ is our alphabet and $n\in\mathbb{Z}^{+}$, we define the following as the powers of $\Sigma$:

$\Sigma^{0}={\lambda}$, where $\lambda$ stands for the empty string.

$\Sigma^{n}=\{xyx\in\Sigma,y\in\Sigma^{{n1}}\}$ ($xy$ is the juxtaposition of $x$ and $y$)
Related:
KleeneStar, Substring, Language, HuffmanCoding, Word
Synonym:
powers of an alphabet
Type of Math Object:
Definition
Major Section:
Reference
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