String

Summary

A string, or word, over an alphabet $\Sigma$ is a finite sequence of symbols of $\Sigma$, such as $0110$ over $\set{0, 1}$. The set $\Sigma^*$ of all strings, with concatenation, is the free monoid on $\Sigma$, with the empty string as identity. Strings are the inputs and outputs of machines such as Turing machines and finite automata. Sets of strings are formal languages.