Hierarchies of Tree Series Transformations Revisited

  • Andreas Maletti
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4036)


Tree series transformations computed by polynomial top-down and bottom-up tree series transducers are considered. The hierarchy of tree series transformations obtained in [Fülöp, Gazdag, Vogler: Hierarchies of Tree Series Transformations. Theoret. Comput. Sci. 314(3), p. 387–429, 2004] for commutative izz-semirings (izz abbreviates idempotent, zero-sum and zero-divisor free) is generalized to arbitrary positive (i.e., zero-sum and zero-divisor free) commutative semirings. The latter class of semirings includes prominent examples such as the natural numbers semiring and the least common multiple semiring, which are not members of the former class.


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  1. 1.
    Kuich, W.: Tree transducers and formal tree series. Acta Cybernet. 14, 135–149 (1999)zbMATHMathSciNetGoogle Scholar
  2. 2.
    Engelfriet, J., Fülöp, Z., Vogler, H.: Bottom-up and top-down tree series transformations. J. Autom. Lang. Combin. 7, 11–70 (2002)zbMATHGoogle Scholar
  3. 3.
    Fülöp, Z., Vogler, H.: Tree series transformations that respect copying. Theory Comput. Systems 36, 247–293 (2003)zbMATHCrossRefGoogle Scholar
  4. 4.
    Kuich, W.: Formal power series over trees. In: Bozapalidis, S. (ed.) Proc. 3rd Int. Conf. Develop. in Lang. Theory, pp. 61–101. Aristotle University of Thessaloniki (1998)Google Scholar
  5. 5.
    Bozapalidis, S.: Equational elements in additive algebras. Theory Comput. Systems 32, 1–33 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Ésik, Z., Kuich, W.: Formal tree series. J. Autom. Lang. Combin. 8, 219–285 (2003)zbMATHGoogle Scholar
  7. 7.
    Borchardt, B., Vogler, H.: Determinization of finite state weighted tree automata. J. Autom. Lang. Combin. 8, 417–463 (2003)zbMATHMathSciNetGoogle Scholar
  8. 8.
    Droste, M., Pech, C., Vogler, H.: A Kleene theorem for weighted tree automata. Theory Comput. Systems 38, 1–38 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Berstel, J., Reutenauer, C.: Recognizable formal power series on trees. Theoret. Comput. Sci. 18, 115–148 (1982)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Borchardt, B.: The Theory of Recognizable Tree Series. PhD thesis, Technische Universität Dresden (2005)Google Scholar
  11. 11.
    Graehl, J., Knight, K.: Training tree transducers. In: Human Lang. Tech. Conf. of the North American Chapter of the Assoc. for Computational Linguistics, pp. 105–112 (2004)Google Scholar
  12. 12.
    Engelfriet, J.: The copying power of one-state tree transducers. J. Comput. System Sci. 25, 418–435 (1982)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Raoult, J.-C.: A survey of tree transductions. In: Nivat, M., Podelski, A. (eds.) Tree Automata and Languages. Elsevier Science, Amsterdam (1992)Google Scholar
  14. 14.
    Fülöp, Z., Gazdag, Z., Vogler, H.: Hierarchies of tree series transformations. Theoret. Comput. Sci. 314, 387–429 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Hebisch, U., Weinert, H.J.: Semirings—Algebraic Theory and Applications in Computer Science. World Scientific, Singapore (1998)zbMATHGoogle Scholar
  16. 16.
    Golan, J.S.: Semirings and their Applications. Kluwer Academic, Dordrecht (1999)zbMATHGoogle Scholar
  17. 17.
    Bozapalidis, S.: Context-free series on trees. Inform. and Comput. 169, 186–229 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Engelfriet, J.: Three hierarchies of transducers. Math. Systems Theory 15, 95–125 (1982)zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Maletti, A.: The power of tree series transducers of type I and II. In: De Felice, C., Restivo, A. (eds.) DLT 2005. LNCS, vol. 3572, pp. 338–349. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  20. 20.
    Engelfriet, J.: Bottom-up and top-down tree transformations—a comparison. Math. Systems Theory 9, 198–231 (1975)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Andreas Maletti
    • 1
  1. 1.Department of Computer ScienceTechnische Universität Dresden 

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