Static Garbage Collection

  • Sebastian ManethEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11601)


We present a method that allows to bound the sizes of intermediate trees in a composition of macro tree transducers. Macro tree transducers are a powerful model of tree translation which, for instance, includes all attribute grammars (seen as tree-to-tree translators). The idea of the method is to change a transducer in the composition so that it does not produce output nodes that will be removed (and ignored) by a subsequent transducer in the composition. This can be considered as a form of static garbage collection, where garbage is never produced by any transducer. We then give three applications of this result and show that (1) compositions of macro tree transducers can be computed in linear time with respect to the sum of sizes of input and output trees, (2) finiteness of ranges of compositions of macro tree transducers is decidable, and (3) the macro tree transducer composition hierarchy collapses when restricted to functions of linear size increase.


  1. 1.
    Deransart, P., Jourdan, M. (eds.): Attribute Grammars and their Applications. LNCS, vol. 461. Springer, Heidelberg (1990). Scholar
  2. 2.
    Engelfriet, J., Inaba, K., Maneth, S.: Linear bounded composition of tree-walking tree transducers: linear size increase and complexity. CoRR abs/1904.09203 (2019).
  3. 3.
    Engelfriet, J., Maneth, S.: Macro tree transducers, attribute grammars, and MSO definable tree translations. Inf. Comput. 154(1), 34–91 (1999). Scholar
  4. 4.
    Engelfriet, J., Maneth, S.: Macro tree translations of linear size increase are MSO definable. SIAM J. Comput. 32(4), 950–1006 (2003). Scholar
  5. 5.
    Engelfriet, J., Vogler, H.: Macro tree transducers. J. Comput. System Sci. 31(1), 71–146 (1985). Scholar
  6. 6.
    Fülöp, Z., Vogler, H.: Syntax-Directed Semantics - Formal Models Based on Tree Transducers. Monographs in Theoretical Computer Science. An EATCS Series. Springer, Heidelberg (1998). Scholar
  7. 7.
    Knuth, D.E.: Semantics of context-free languages. Math. Syst. Theory 2(2), 127–145 (1968). Scholar
  8. 8.
    Maneth, S.: The complexity of compositions of deterministic tree transducers. In: Agrawal, M., Seth, A. (eds.) FSTTCS 2002. LNCS, vol. 2556, pp. 265–276. Springer, Heidelberg (2002). Scholar
  9. 9.
    Maneth, S.: The macro tree transducer hierarchy collapses for functions of linear size increase. In: Pandya, P.K., Radhakrishnan, J. (eds.) FSTTCS 2003. LNCS, vol. 2914, pp. 326–337. Springer, Heidelberg (2003). Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.FB3 - InformatikUniversität BremenBremenGermany

Personalised recommendations