Relating Tree Series Transducers and Weighted Tree Automata

  • Andreas Maletti
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3340)


In this paper we implement bottom-up tree series transducers (tst) over the semiring \(\mathcal{A}\) with the help of bottom-up weighted tree automata (wta) over an extension of \(\mathcal{A}\). Therefore we firstly introduce bottom-up DM-monoid weighted tree automata (DM-wta), which essentially are wta using an operation symbol of a DM-monoid instead of a semiring element as transition weight. Secondly, we show that DM-wta are indeed a generalization of tst (using pure substitution). Thirdly, given a DM-wta we construct a semiring \(\mathcal{A}\) along with a wta such that the wta computes a formal representation of the semantics of the DM-wta.

Finally, we demonstrate the applicability of our presentation result by deriving a pumping lemma for deterministic tst as well as deterministic DM-wta from a pumping lemma for deterministic wta.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Berstel, J.: Transductions and Context-Free Languages. Teubner, Stuttgart (1979)Google Scholar
  2. 2.
    Borchardt, B.: A pumping lemma and decidability problems for recognizable tree series. Acta Cybernetica (2004) (to appear)Google Scholar
  3. 3.
    Bozapalidis, S.: Equational elements in additive algebras. Theory of Computing Systems 32, 1–33 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Comon, H., Dauchet, M., Gilleron, R., Jacquemard, F., Lugiez, D., Tison, S., Tommasi, M.: Tree automata – techniques and applications (1997) Available on,
  5. 5.
    Eilenberg, S.: Automata, Languages, and Machines – Volume A. Pure and Applied Mathematics, vol. 59. Academic Press, London (1974)Google Scholar
  6. 6.
    Engelfriet, J.: Some open questions 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, London (1980)Google Scholar
  7. 7.
    Engelfriet, J., Fülöp, Z., Vogler, H.: Bottom-up and top-down tree series transformations. Journal of Automata, Languages and Combinatorics 7(1), 11–70 (2002)zbMATHMathSciNetGoogle Scholar
  8. 8.
    Fülöp, Z., Vogler, H.: Tree series transformations that respect copying. Theory of Computing Systems 36, 247–293 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Kuich, W.: Formal power series over trees. In: Bozapalidis, S. (ed.) Proceedings of 3rd DLT 1997, pp. 61–101. Aristotle University of Thessaloniki (1997)Google Scholar
  10. 10.
    Kuich, W.: Tree transducers and formal tree series. Acta Cybernetica 14, 135–149 (1999)zbMATHMathSciNetGoogle Scholar
  11. 11.
    Kuich, W., Salomaa, A.: Semirings, Automata, Languages. EATCS Monographs on Theoretical Computer Science, vol. 5. Springer, Heidelberg (1986)zbMATHGoogle Scholar
  12. 12.
    Rounds, W.C.: Mappings and grammars on trees. In: Mathematical Systems Theory, vol. 4, pp. 257–287 (1970)Google Scholar
  13. 13.
    Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages, vol. 1. Springer, Heidelberg (1997)zbMATHGoogle Scholar
  14. 14.
    Schützenberger, M.P.: Certain elementary families of automata. In: Proceedings of Symposium on Mathematical Theory of Automata, pp. 139–153. Polytechnic Institute of Brooklyn (1962)Google Scholar
  15. 15.
    Thatcher, J.W.: Generalized2 sequential machine maps. Journal of Computer and System Sciences 4, 339–367 (1970)zbMATHMathSciNetCrossRefGoogle Scholar
  16. 16.
    Thatcher, J.W., Wagner, E.G., Wright, J.B.: Initial algebra semantics and continuous algebra. Journal of the ACM 24, 68–95 (1977)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Andreas Maletti
    • 1
  1. 1.Fakultät InformatikTechnische Universität DresdenDresdenGermany

Personalised recommendations