Deciding Equivalence of Linear Tree-to-Word Transducers in Polynomial Time

  • Adrien Boiret
  • Raphaela PalentaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9840)


We show that the equivalence of linear top-down tree-to-word transducers is decidable in polynomial time. Linear tree-to-word transducers are non-copying but not necessarily order-preserving and can be used to express XML and other document transformations. The result is based on a partial normal form that provides a basic characterization of the languages produced by linear tree-to-word transducers.


Tree transducer Deciding equivalence Partial normal form 



We would like to thank the reviewers for their very helpful comments.


  1. 1.
    Boiret, A.: Normal form on linear tree-to-word transducers. In: Dediu, A.-H., et al. (eds.) Language and Automata Theory and Applications. LNCS, vol. 9618, pp. 439–451. Springer, Heidelberg (2016)CrossRefGoogle Scholar
  2. 2.
    Engelfriet, J.: Some open question and recent results on tree transducers and tree languages. In: Book, R.V. (ed.) Formal Language Theory, Perspectives and Open Problems, pp. 241–286. Academic Press, New York (1980)Google Scholar
  3. 3.
    Engelfriet, J., Maneth, S.: Macro tree translations of linear size increase are MSO definable. SIAM J. Comput. 32(4), 950–1006 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Engelfriet, J., Maneth, S.: The equivalence problem for deterministic MSO tree transducers is decidable. Inf. Process. Lett. 100(5), 206–212 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Engelfriet, J., Rozenberg, G., Slutzki, G.: Tree transducers, L systems and two-way machines. In: Proceedings of the Tenth Annual ACM Symposium on Theory of Computing, pp. 66–74. ACM (1978)Google Scholar
  6. 6.
    Engelfriet, J., Vogler, H.: Macro tree transducers. J. Comput. Syst. Sci. 31(1), 71–146 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Laurence, G., Lemay, A., Niehren, J., Staworko, S., Tommasi, M.: Normalization of sequential top-down tree-to-word transducers. In: Dediu, A.-H., Inenaga, S., Martín-Vide, C. (eds.) LATA 2011. LNCS, vol. 6638, pp. 354–365. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  8. 8.
    Lemay, A., Maneth, S., Niehren, J.: A learning algorithm for top-down XML transformations. In: Proceedings of the Twenty-Ninth ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, pp. 285–296 (2010)Google Scholar
  9. 9.
    Lohrey, M.: The Compressed Word Problem for Groups. Springer, New York (2014)CrossRefzbMATHGoogle Scholar
  10. 10.
    Maneth, S., Seidl, H.: Deciding equivalence of top-down XML transformations in polynomial time. In: Programming Language Technologies for XML, pp. 73–79 (2007)Google Scholar
  11. 11.
    Plandowski, W.: The complexity of the morphism equivalence problem for context-free languages. Ph.D. thesis, Warsaw University (1995)Google Scholar
  12. 12.
    Seidl, H., Maneth, S., Kemper, G.: Equivalence of deterministic top-down tree-to-string transducers is decidable. In: IEEE 56th Annual Symposium on Foundations of Computer Science, pp. 943–962 (2015)Google Scholar
  13. 13.
    Staworko, S., Laurence, G., Lemay, A., Niehren, J.: Equivalence of deterministic nested word to word transducers. In: Charatonik, W., Gębala, M., Kutyłowski, M. (eds.) FCT 2009. LNCS, vol. 5699, pp. 310–322. Springer, Heidelberg (2009)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.CRIStALUniversity Lille 1Villeneuve d’Ascq CedexFrance
  2. 2.Department of InformaticsTechnical University of MunichGarchingGermany

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