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In this paper I would like to witness the mathematical inventiveness of G.Rauzy through personnal exchanges I had with him. The objects that will emergewill be used to treat the decidability of the HD 0 L $\omega$-equivalence andperiodicity problems in the primitive case.

HD0L-$\omega$-equivalence and periodicity problems in the primitive case (to the memory of G. Rauzy)