On the decomposition of finite-valued streaming string transducers

Abstract : We prove the following decomposition theorem: every 1-register streaming string transducer that associates a uniformly bounded number of outputs with each input can be effectively decomposed as a finite union of functional 1-register streaming string transducers. This theorem relies on a combinatorial result by Kortelainen concerning word equations with iterated factors. Our result implies the decidability of the equivalence problem for the considered class of transducers. This can be seen as a first step towards proving a more general decomposition theorem for streaming string transducers with multiple registers.
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Paul Gallot, Anca Muscholl, Gabriele Puppis, Sylvain Salvati. On the decomposition of finite-valued streaming string transducers. 34th International Symposium on Theoretical Aspects of Computer Science (STACS), Mar 2017, Hannover, Germany. ⟨10.4230/LIPIcs⟩. ⟨hal-01431250⟩

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