Aperiodic String Transducers

  • Luc Dartois
  • Ismaël Jecker
  • Pierre-Alain Reynier
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9840)


Regular string-to-string functions enjoy a nice triple characterization through deterministic two-way transducers (\(\mathrm {2DFT}\)), streaming string transducers (\(\mathrm {SST}\)) and \(\mathrm {MSO}\) definable functions. This result has recently been lifted to \(\mathrm {FO}\) definable functions, with equivalent representations by means of aperiodic \(\mathrm {2DFT}\) and aperiodic 1-bounded \(\mathrm {SST}\), extending a well-known result on regular languages. In this paper, we give three direct transformations: (i) from 1-bounded \(\mathrm {SST}\) to \(\mathrm {2DFT}\), (ii) from \(\mathrm {2DFT}\) to copyless \(\mathrm {SST}\), and (iii) from k-bounded to 1-bounded \(\mathrm {SST}\). We give the complexity of each construction and also prove that they preserve the aperiodicity of transducers. As corollaries, we obtain that \(\mathrm {FO}\) definable string-to-string functions are equivalent to \(\mathrm {SST}\) whose transition monoid is finite and aperiodic, and to aperiodic copyless \(\mathrm {SST}\).


Transducer Streaming Two-way Monoid Aperiodic 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Luc Dartois
    • 1
  • Ismaël Jecker
    • 1
  • Pierre-Alain Reynier
    • 2
  1. 1.Université Libre de BruxellesBrusselBelgium
  2. 2.Aix-Marseille Université, CNRS, LIF UMR 7279MarseilleFrance

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