On the weighted mean of a pair of strings

String matching and string edit distance are fundamental concepts in structural pattern recognition. In this paper, the weighted mean of a pair of strings is introduced. Given two strings, x and y, where d(x, y) is the edit distance of x and y the weighted mean of x and y is a string z that has edit distances d(x, z) and d(z, y) to x and y, respectively, such that d(x, z) + d(z, y) = d(x, y). We'll show formal properties of the weighted mean, describe a procedure for its computation, and give practical examples.