String

Definition

A string (or word) over an Alphabet $\Sigma$ is a finite sequence of symbols from $\Sigma$.
The set of all strings over $\Sigma$ is denoted ${\Sigma }^{\ast }$.
The empty string is denoted $\epsilon$ and has length 0.

Concatenation

Given strings $u,v\in {\Sigma }^{\ast }$, their concatenation $uv$ is the sequence of symbols in $u$ followed by the symbols in $v$.