$$$$

Strings

An alphabet is any finite set, whose members are called letters (equivalently: symbols or characters). We typically use $\mathrm{\Sigma }$ to denote a generic alphabet and $a,b,c,d$ as variables that stand for the letters.

A string (equivalently: word) over an alphabet $\mathrm{\Sigma }$ is a finite sequence of characters from $\mathrm{\Sigma }$. The sequence may be empty, and we write the empty string as $ϵ$. We typically use $u,v,w,x,y,z$ as variables that stand for a string.

The set of all strings over the alphabet $\mathrm{\Sigma }$ is written ${\mathrm{\Sigma }}^{\ast }$, this always includes $ϵ$. We will refer to a set of strings as a language.