The EditDistance(s,t) command returns an integer measure of the distance between the two strings s and t.

The edit distance between two strings s and t, is defined to be the difference between the sum of their lengths and twice the length of the longest common subsequence of s and t. If strings s and t have respective lengths m and n, then the edit distance is defined to be $m+n-2\mathrm{length}\left(\mathrm{LongestCommonSubSequence}\left(s\,t\right)\right)$. It is related to the Levenshtein metric, which is sometimes also called the edit distance.

For a different notion of the distance between two strings, see StringTools[HammingDistance] and StringTools[Levenshtein].

All of the StringTools package commands treat strings as (null-terminated) sequences of $8$-bit (ASCII) characters.  Thus, there is no support for multibyte character encodings, such as unicode encodings.

$\mathbf{use}\mathrm{StringTools}\mathbf{in}\mathrm{EditDistance}\left(''Mathematics''\,''Mathematische''\right)\mathbf{end\; use}$

$4$

$\mathrm{with}\left(\mathrm{StringTools}\right)\:$

$\mathrm{EditDistance}\left(''abc''\,''abd''\right)$

$2$

$\mathrm{EditDistance}\left(''abc''\,''abcd''\right)$

$1$

$\mathrm{EditDistance}\left(''Elisabeth''\,''Elyse''\right)$

$6$

$\mathrm{EditDistance}\left(''Connor''\,''Constance''\right)$

$7$

$s≔\mathrm{Random}\left(1000\,'\mathrm{lower}'\right)\:$

$t≔\mathrm{Random}\left(1000\,'\mathrm{lower}'\right)\:$

$u≔\mathrm{Random}\left(1000\,'\mathrm{lower}'\right)\:$

$\mathrm{EditDistance}\left(s\,t\right)$

$1352$

$\mathrm{EditDistance}\left(s\,u\right)+\mathrm{EditDistance}\left(u\,t\right)$

$2746$