Abstract
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.
A. Boiret—This work was partially supported by a grant from CPER Nord-Pas de Calais/FEDER DATA Advanced data science and technologies 2015–2020.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
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)
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)
Engelfriet, J., Maneth, S.: Macro tree translations of linear size increase are MSO definable. SIAM J. Comput. 32(4), 950–1006 (2003)
Engelfriet, J., Maneth, S.: The equivalence problem for deterministic MSO tree transducers is decidable. Inf. Process. Lett. 100(5), 206–212 (2006)
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)
Engelfriet, J., Vogler, H.: Macro tree transducers. J. Comput. Syst. Sci. 31(1), 71–146 (1985)
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)
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)
Lohrey, M.: The Compressed Word Problem for Groups. Springer, New York (2014)
Maneth, S., Seidl, H.: Deciding equivalence of top-down XML transformations in polynomial time. In: Programming Language Technologies for XML, pp. 73–79 (2007)
Plandowski, W.: The complexity of the morphism equivalence problem for context-free languages. Ph.D. thesis, Warsaw University (1995)
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)
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)
Acknowledgement
We would like to thank the reviewers for their very helpful comments.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Boiret, A., Palenta, R. (2016). Deciding Equivalence of Linear Tree-to-Word Transducers in Polynomial Time. In: Brlek, S., Reutenauer, C. (eds) Developments in Language Theory. DLT 2016. Lecture Notes in Computer Science(), vol 9840. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53132-7_29
Download citation
DOI: https://doi.org/10.1007/978-3-662-53132-7_29
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-53131-0
Online ISBN: 978-3-662-53132-7
eBook Packages: Computer ScienceComputer Science (R0)