In order to support the next hypothesis we will make on analogies on strings of symbols, let us list a small number of analogies in English: hypothesis : hypotheses = thesis : theses leaf : leaves = calf : calves give : gave = sing : sang inexact : exact = incapable : capable plus some true analogies but with no meaning in language: aa : aaaa = aaaa : aaaaaa 2 give : gave = bid : bad walk : walked = go : goed 3 and some counter-examples (noted with 6 =): aaaa : bbbb 6 = cccc : dddd 4 dfhka : bzvmbz 6 = bzvmbz : dfhka 2 This analogy holds independently of the truth (or falsity of) aa : aaaa = aaaa : aaaaaaaa ( a 2 : a 4 = a 4 : a 8 ).
a language like fa 2 n =n 2 INg is not a language of analogical strings, as it does not have the bounded growth property.