Substring

Prefix

A string ${\displaystyle p}$ is a prefix of a string ${\displaystyle t}$ if there exists a string ${\displaystyle s}$ such that ${\displaystyle t=ps}$. A proper prefix of a string is not equal to the string itself; some sources in addition restrict a proper prefix to be non-empty. A prefix can be seen as a special case of a substring.

Example: The string ban is equal to a prefix (and substring and subsequence) of the string banana:

banana ||| ban

The square subset symbol is sometimes used to indicate a prefix, so that ${\displaystyle p⊑t}$ denotes that ${\displaystyle p}$ is a prefix of ${\displaystyle t}$. This defines a binary relation on strings, called the prefix relation, which is a particular kind of prefix order.

Suffix

A string ${\displaystyle s}$ is a suffix of a string ${\displaystyle t}$ if there exists a string ${\displaystyle p}$ such that ${\displaystyle t=ps}$. A proper suffix of a string is not equal to the string itself. A more restricted interpretation is that it is also not empty. A suffix can be seen as a special case of a substring.

Example: The string nana is equal to a suffix (and substring and subsequence) of the string banana:

banana |||| nana

A suffix tree for a string is a trie data structure that represents all of its suffixes. Suffix trees have large numbers of applications in string algorithms. The suffix array is a simplified version of this data structure that lists the start positions of the suffixes in alphabetically sorted order; it has many of the same applications.

Border

A border is suffix and prefix of the same string, e.g. "${\displaystyle \mathtt{\text{bab}}}$" is a border of "${\displaystyle \mathtt{\text{babab}}}$" (and also of "${\displaystyle \mathtt{\text{baboon}}\mathtt{\text{eating}}\mathtt{\text{a}}\mathtt{\text{kebab}}}$").

Superstring

A superstring of a finite set ${\displaystyle P}$ of strings is a single string that contains every string in ${\displaystyle P}$ as a substring. For example, ${\displaystyle \mathtt{\text{bcclabccefab}}}$ is a superstring of ${\displaystyle P=\{\mathtt{\text{abcc}},\mathtt{\text{efab}},\mathtt{\text{bccla}}\}}$, and ${\displaystyle \mathtt{\text{efabccla}}}$ is a shorter one. Concatenating all members of ${\displaystyle P}$, in arbitrary order, always obtains a trivial superstring of ${\displaystyle P}$. Finding superstrings whose length is as small as possible is a more interesting problem.

A string that contains every possible permutation of a specified character set is called a superpermutation.