Definition:Prefix

Definition

A string $T$ is a prefix of a string $S$ if and only if $S$ can be formed by concatenating $T$ with another string $T'$:

$S = TT'$

Proper Prefix

A proper prefix of a string $S$ is a prefix of $S$ which does not equal the whole of $S$.

Also known as

A prefix is referred to by some sources as an initial part.

Examples

Arbitrary Example

Let $abc$ be a string.

Then the prefixes of $abc$ are:

$\epsilon$, $a$, $ab$ and $abc$

where $\epsilon$ is the null string.

Also see

• Definition:Suffix

• Prefix of String is Substring

• Results about prefixes can be found here.

Sources

• 1979: John E. Hopcroft and Jeffrey D. Ullman: Introduction to Automata Theory, Languages, and Computation ... (previous) ... (next): Chapter $1$: Preliminaries: $1.1$ Strings, Alphabets and Languages
• 1996: H. Jerome Keisler and Joel Robbin: Mathematical Logic and Computability ... (previous) ... (next): $\S 1.3$: Induction on Length of Wffs: Proposition $1.3.2$