. Preuve, Prenons un dST2W M Comme le montre le théorème 15, il est possible de construire un edST2W M ? équivalent, ayant un nombre fini d'états. Le lemme 24, quant à lui, nous assure qu'il existe une transformation ? = M ? appartenant à la classe des ST Ws dont l'index de Myhill-Nerode est égal au nombre d'états, Il faut que Cano(? ) soit l'unique edST2W minimal décrivant ? , ce qui est prouvé par le corrolaire 5. ((3) ? (1)) est trivial

. Preuve, Remarquons tout d'abord que, S étant caractéristique pour ? et p appartenant à resChemins(? ), (f, i) ?1 dom(S) est discriminant pour ? et p?(f, i), pour tout 1 ? i ? k. En particulier, s = min Arbre (dom(S))

. Et-de-la-même-manière-s-i-=-min-arbre, (? )) pour 1 ? i ? k. Nous pouvons maintenant prouver ce lemme par induction sur i, en allant de k à 1. Pour la suite de la preuve, le mot w i représente w i = lcp({? i (t i )?u i ?. . .? ? k (t k ) ? u k t j ? (f, j) ?1 dom(S)}) Nous allons montrer que q i+1 = ? implique que w i = ?. Pour cela

?. ?u-i, ?im(? k )?u k ) est un préfixe de lcp(w, u i ) = ?. Donc, Cela implique que lcp(im

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