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We study additive distances and quasi-distances between words. We show that every additive distance is finite. We then prove that every additive quasi-distance is regularity-preserving, that is, the neighborhood of any radius of a regular language with respect to an additive quasi-distance is regular. Finally, similar results will be proven for context-free, computable and computably enumerable languages.

Additive Distances and Quasi_Distances Between Words