Definition:Substring

Definition

Let $\LL$ be a formal language with alphabet $\AA$.

Let $S$ be a string in $\AA$.

Let $T$ be a string in $\AA$ such that:

$S = S_1 T S_2$

where:

$S_1$ and $S_2$ are strings in $\AA$ (possibly null)

$S_1 T S_2$ is the concatenation of $S_1$, $T$ and $S_2$.

Then $T$ is called a substring of $S$.

Proper Substring

A proper substring of a string $S$ in $\AA$ is a substring of $S$ which is specifically not equal to $S$.

Also see

• String is Substring of Itself

• Prefix of String is Substring

• Results about substrings can be found here.