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Weighted Bottom-Up and Top-Down Tree Transformations Are Incomparable

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Implementation and Application of Automata (CIAA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14151))

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Abstract

Weighted bottom-up and top-down tree transformations over commutative semirings are investigated. It is demonstrated that if the range of a weighted bottom-up tree transformation is well-defined (i.e., for every output tree there are only finitely many input trees that can transform to the output tree with nonzero weight, so that all involved sums remain finite), then the range is hom-regular, which means that it is the image of a regular weighted tree language under a tree homomorphism. Additionally, the strictness of the first level of the weighted bottom-up and top-down tree transformation hierarchy is proved, which was open for any ring.

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References

  1. Baker, B.S.: Tree transductions and families of tree languages. In: Proceedings of the STOC, pp. 200–206 (1973). https://doi.org/10.1145/800125.804051

  2. Doner, J.: Tree acceptors and some of their applications. J. Comput. Syst. Sci. 4(5), 406–451 (1970). https://doi.org/10.1016/S0022-0000(70)80041-1

    Article  MathSciNet  MATH  Google Scholar 

  3. Engelfriet, J.: Bottom-up and top-down tree transformations – a comparison. Math. Syst. Theory 9(3), 198–231 (1975). https://doi.org/10.1007/BF01704020

    Article  MathSciNet  MATH  Google Scholar 

  4. Engelfriet, J.: Three hierarchies of transducers. Math. Syst. Theory 15(2), 95–125 (1982). https://doi.org/10.1007/BF01786975

    Article  MathSciNet  MATH  Google Scholar 

  5. Engelfriet, J., Fülöp, Z., Vogler, H.: Bottom-up and top-down tree series transformations. J. Autom. Lang. Comb. 7(1), 11–70 (2002). https://doi.org/10.25596/jalc-2002-011

  6. Fülöp, Z., Gazdag, Z., Vogler, H.: Hierarchies of tree series transformations. Theoret. Comput. Sci. 314(3), 387–429 (2004). https://doi.org/10.1016/j.tcs.2004.01.001

    Article  MathSciNet  MATH  Google Scholar 

  7. Fülöp, Z., Vogler, H.: Weighted tree transducers. J. Autom. Lang. Comb. 9(1), 31–54 (2004). https://doi.org/10.25596/jalc-2004-031

  8. Fülöp, Z., Vogler, H.: Weighted tree automata and tree transducers. In: Droste, M., Kuich, W., Vogler, H. (eds.) Handbook of Weighted Automata, chap. 9, pp. 313–403. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-01492-5_9

  9. Godoy, G., Giménez, O.: The HOM problem is decidable. J. ACM 60(4) (2013). https://doi.org/10.1145/2508028.2501600

  10. Golan, J.S.: Semirings and their Applications. Kluwer Academic, Dordrecht (1999). https://doi.org/10.1007/978-94-015-9333-5

  11. Hebisch, U., Weinert, H.J.: Semirings: Algebraic Theory and Applications in Computer Science, Series in Algebra, vol. 5. World Scientific (1998). https://doi.org/10.1142/3903

  12. Jurafsky, D., Martin, J.H.: Speech and Language Processing, 2nd edn. Prentice Hall, Hoboken (2008)

    Google Scholar 

  13. Kuich, W.: Tree transducers and formal tree series. Acta Cybernet. 14(1), 135–149 (1999)

    MathSciNet  MATH  Google Scholar 

  14. Maletti, A.: Hierarchies of tree series transformations revisited. In: Ibarra, O.H., Dang, Z. (eds.) DLT 2006. LNCS, vol. 4036, pp. 215–225. Springer, Heidelberg (2006). https://doi.org/10.1007/11779148_20

    Chapter  Google Scholar 

  15. Maletti, A., Nász, A.T.: Weighted tree automata with constraints. arXiv (2023). https://doi.org/10.48550/ARXIV.2302.03434

  16. Thatcher, J.W.: Characterizing derivation trees of context-free grammars through a generalization of finite automata theory. J. Comp. Syst. Sci. 1(4), 317–322 (1967). https://doi.org/10.1016/S0022-0000(67)80022-9

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Universität Leipzig, PO box 100 920, 04009, Leipzig, Germany

    Andreas Maletti & Andreea-Teodora Nász

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  1. Andreas Maletti
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  2. Andreea-Teodora Nász
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Correspondence to Andreas Maletti .

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Editors and Affiliations

  1. Eastern Mediterranean University, Famagusta, Cyprus

    Benedek Nagy

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Maletti, A., Nász, AT. (2023). Weighted Bottom-Up and Top-Down Tree Transformations Are Incomparable. In: Nagy, B. (eds) Implementation and Application of Automata. CIAA 2023. Lecture Notes in Computer Science, vol 14151. Springer, Cham. https://doi.org/10.1007/978-3-031-40247-0_16

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  • DOI: https://doi.org/10.1007/978-3-031-40247-0_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-40246-3

  • Online ISBN: 978-3-031-40247-0

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