Streaming Ranked-Tree-to-String Transducers

  • Yuta TakahashiEmail author
  • Kazuyuki Asada
  • Keisuke Nakano
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11601)


Streaming tree transducers with single-use restriction (\(\mathrm {STT}_{\mathrm {sur}}\text {s}\)) were introduced by Alur and D’Antoni as an analyzable, executable, and expressive model for transforming unranked ordered trees in a single pass. The equivalence problem of \(\mathrm {STT}_{\mathrm {sur}}\text {s}\) is decidable because their class is as expressive as the class of MSO-definable tree transformations. In this paper, we present streaming ranked-tree-to-string transducers (\(\mathrm {SRTSTs}\)), based on \(\mathrm {STT}_{\mathrm {sur}}\text {s}\): \(\mathrm {SRTSTs}\) are released from the single-use restriction while their input and output are restricted to ranked trees and strings, respectively. We show that the expressiveness of \(\mathrm {SRTSTs}\) coincides with that of deterministic top-down tree transducers with regular look-ahead (\(\mathrm {yDT}^{\mathrm {R}}\mathrm {s}\)), whose equivalence problem is known to be decidable. Our proof is done by constructing equivalent transducers in both directions.


Ranked trees Streaming transducers Expressiveness Equivalence 



We thank anonymous referees for useful comments. This work was supported by JSPS KAKENHI Grant Numbers JP17K00007, JP17H06099, JP18H04093, and JP18K11156.


  1. 1.
    Alur, R., D’Antoni, L.: Streaming tree transducers. J. ACM 64(5), 31:1–31:55 (2017)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Alur, R., Černý, P.: Streaming transducers for algorithmic verification of single-pass list-processing programs. In: POPL 2011, pp. 599–610. ACM (2011)Google Scholar
  3. 3.
    Comon, H., Dauchet, M., Gilleron, R., Löding, C., Jacquemard, F., Lugiez, D., Tison, S., Tommasi, M.: Tree Automata Techniques and Applications (2007)Google Scholar
  4. 4.
    Engelfriet, J.: Top-down tree transducers with regular look-ahead. Math. Syst. Theory 10(1), 289–303 (1976)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Engelfriet, J.: Some open questions and recent results on tree transducers and tree languages. In: Formal Language Theory, pp. 241–286. Academic Press (1980)Google Scholar
  6. 6.
    Engelfriet, J., Maneth, S.: Macro tree transducers, attribute grammars, and MSO definable tree translations. Inform. Comput. 154(1), 34–91 (1999)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Engelfriet, J., Maneth, S.: The equivalence problem for deterministic MSO tree transducers is decidable. Inform. Process. Lett. 100(5), 206–212 (2006)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Engelfriet, J., Rozenberg, G., Slutzki, G.: Tree transducers, L systems, and two-way machines. J. Comput. Syst. Sci. 20(2), 150–202 (1980)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Filiot, E., Reynier, P.A.: Copyful streaming string transducers. In: Hague, M., Potapov, I. (eds.) Reachability Problems. LNCS, vol. 10506, pp. 75–86. Springer, Cham (2017). Scholar
  10. 10.
    Nakano, K., Mu, S.-C.: A pushdown machine for recursive XML processing. In: Kobayashi, N. (ed.) APLAS 2006. LNCS, vol. 4279, pp. 340–356. Springer, Heidelberg (2006). Scholar
  11. 11.
    Seidl, H., Maneth, S., Kemper, G.: Equivalence of deterministic top-down tree-to-string transducers is decidable. In: FOCS 2015, pp. 943–962. IEEE (2015)Google Scholar
  12. 12.
    Seidl, H., Maneth, S., Kemper, G.: Equivalence of deterministic top-down tree-to-string transducers is decidable. J. ACM 65(4), 21:1–21:30 (2018)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Staworko, S., Laurence, G., Lemay, A., Niehren, J.: Equivalence of deterministic nested word to word transducers. In: FCT 2009. LNCS, vol. 5699, pp. 310–322. Springer, Heidelberg (2009). Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Yuta Takahashi
    • 1
    Email author
  • Kazuyuki Asada
    • 2
  • Keisuke Nakano
    • 2
  1. 1.The University of Electro-CommunicationsChofuJapan
  2. 2.Tohoku UniversitySendaiJapan

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