Equivalence of Symbolic Tree Transducers

  • Vincent HugotEmail author
  • Adrien Boiret
  • Joachim Niehren
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10396)


Symbolic tree transducers are programs that transform data trees with an infinite signature. In this paper, we show that the equivalence problem of deterministic symbolic top-down tree transducers (DTop) can be reduced to that of classical DTop. As a consequence the equivalence of two symbolic DTop can be decided in NExpTime, when assuming that all operations related to the processing of data values are in PTime. This result can be extended to symbolic DTop with lookahead and thus to deterministic symbolic bottom-up tree transducers.


  1. 1.
    Baker, B.S.: Composition of top-down and bottom-up tree transductions. Inf. Control 41(2), 186–213 (1979)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Boiret, A.: Normalization and learning of transducers on trees and words. Ph.D. thesis, Lille University, France (2016)Google Scholar
  3. 3.
    Bojańczyk, M.: Transducers with origin information. In: Esparza, J., Fraigniaud, P., Husfeldt, T., Koutsoupias, E. (eds.) ICALP 2014. LNCS, vol. 8573, pp. 26–37. Springer, Heidelberg (2014). doi: 10.1007/978-3-662-43951-7_3 Google Scholar
  4. 4.
    Choffrut, C.: Minimizing subsequential transducers: a survey. Theor. Comput. Sci. 292(1), 131–143 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Comon, H., Dauchet, M., Gilleron, R., Löding, C., Jacquemard, F., Lugiez, D., Tison, S., Tommasi, M.: Tree automata techniques and applications (2007). Accessed 12th October 2007
  6. 6.
    Elgot, C.C., Mezei, J.E.: On relations defined by generalized finite automata. IBM J. Res. Dev. 9(1), 47–68 (1965)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Engelfriet, J.: Bottom-up and top-down tree transformations - a comparison. Math. Syst. Theor. 9(3), 198–231 (1975)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Engelfriet, J.: Top-down tree transducers with regular look-ahead. Math. Syst. Theor. 10, 289–303 (1977)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Engelfriet, J.: Some Open Questions and Recent Results on Tree Transducers and Tree Languages, pp. 241–286. Academic Press, Cambridge (1980)Google Scholar
  10. 10.
    Engelfriet, J., Maneth, S.: Macro tree translations of linear size increase are MSO definable. SIAM J. Comput. 32(4), 950–1006 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Engelfriet, J., Maneth, S., Seidl, H.: Deciding equivalence of top-down XML transformations in polynomial time. J. Comput. Syst. Sci. 75(5), 271–286 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Engelfriet, J., Vogler, H.: Macro tree transducers. J. Comput. Syst. Sci. 31(1), 71–146 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Ésik, Z.: On functional tree transducers. In: FCT, pp. 121–127 (1979)Google Scholar
  14. 14.
    Ésik, Z.: Decidability results concerning tree transducers II. Acta Cybern. 6(3), 303–314 (1983)MathSciNetzbMATHGoogle Scholar
  15. 15.
    Fülöp, Z., Vogler, H.: Forward and backward application of symbolic tree transducers. Acta Inf. 51(5), 297–325 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Lemay, A., Maneth, S., Niehren, J.: A learning algorithm for top-down XML transformations. In: PODS, pp. 285–296. ACM (2010)Google Scholar
  17. 17.
    Maneth, S.: Equivalence problems for tree transducers: a brief survey. In: Ésik, Z., Fülöp, Z. (eds.) AFL. EPTCS, vol. 151, pp. 74–93 (2014)Google Scholar
  18. 18.
    Seidl, H., Maneth, S., Kemper, G.: Equivalence of deterministic top-down tree-to-string transducers is decidable. In: FOCS, pp. 943–962 (2015)Google Scholar
  19. 19.
    Veanes, M., Bjørner, N.: Foundations of finite symbolic tree transducers. EATCS 105, 141–173 (2011)MathSciNetzbMATHGoogle Scholar
  20. 20.
    Veanes, M., Bjørner, N.: Symbolic tree transducers. In: Clarke, E., Virbitskaite, I., Voronkov, A. (eds.) PSI 2011. LNCS, vol. 7162, pp. 377–393. Springer, Heidelberg (2012). doi: 10.1007/978-3-642-29709-0_32 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Vincent Hugot
    • 2
    • 3
    Email author
  • Adrien Boiret
    • 2
    • 3
  • Joachim Niehren
    • 1
    • 3
  1. 1.InriaLilleFrance
  2. 2.University of LilleLilleFrance
  3. 3.Links Project (Inria & Cristal Lab - UMR CNRS 9189)LilleFrance

Personalised recommendations