String Transformations Preserving Analogies

This paper examines the following problem: which transformations on strings preserve analogy? For instance, consider the analogy putra: putera:: putri: puteri.
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1Indonesian: prince/son, princess/daughter in two possible spellings. If we systematically reduplicate the characters in the strings (ppuuttrraa: ppuutteerraa:: ppuuttrrii: ppuutteerrii), or systematically insert a space between each character in the strings (p.u.t.r.a: p.u.t.e.r.a:: p.u.t.r.i: p.u.t.e.r.i), the analogies between the transformed strings still hold. The analogies considered are formal analogies of commutation between strings of characters, the definition of which makes use of LCS distance. Experiments on more than 16 million formal linguistic examples confirm several theoretical results, invalidate some hypotheses, and allow to test interesting conjectures.