We model the edit distance as a function in a labeling space. A labeling space is an Euclidean space where coordinates are the edit costs. Through this model, we de¯ne a class of cost. A class of cost is a region in the labeling space that all the edit costs have the same optimal labeling. Moreover, we characterize the distance value through the labeling space. This new point of view of the edit distance gives us the opportunity of de¯ning some interesting properties that are useful for a better understanding of the edit distance. Finally, we show the usefulness of these properties through some applications.