Résumé | I will present some preliminary results towards a proof of a decomposition theorem for streaming string transducers (SSTs). Roughly, the conjectured decomposition theorem states that every SST that associates at most k outputs to each input can be effectively decomposed as a finite union of functional SSTs. Such a result would imply, among other things, the decidability of the equivalence problem for the considered class of transducers as well as a correspondence with the classical two-way transducers. I will present a proof of this decomposition theorem in the special case of SSTs with 1 register. The proof heavily relies on a combinatorial result by Kortelainen concerning word equations with iterated factors. |