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Largest Common Prefix of a Regular Tree Language

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Fundamentals of Computation Theory (FCT 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11651))

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Abstract

A family of tree automata of size n is presented such that the size of the largest common prefix (lcp) tree of all accepted trees is exponential in n. Moreover, it is shown that this prefix tree is not compressible via DAGs (directed acyclic graphs) or tree straight-line programs. We also show that determining whether or not the lcp trees of two given tree automata are equal is coNP-complete; the result holds even for deterministic bottom-up tree automata accepting finite tree languages. These results are in sharp contrast to the case of context-free string grammars.

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Notes

  1. 1.

    We define here monadic TSLPs in normal form [6] which makes no difference with respect to succinctness; see [6].

References

  1. Choffrut, C.: Minimizing subsequential transducers: a survey. Theor. Comput. Sci. 292(1), 131–143 (2003)

    Article  MathSciNet  Google Scholar 

  2. Comon, H., et al.: Tree automata techniques and applications (2007). http://tata.gforge.inria.fr/

  3. Engelfriet, J., Maneth, S., Seidl, H.: Deciding equivalence of top-down XML transformations in polynomial time. J. Comput. Syst. Sci. 75(5), 271–286 (2009)

    Article  MathSciNet  Google Scholar 

  4. Ganardi, M., Hucke, D., Jez, A., Lohrey, M., Noeth, E.: Constructing small tree grammars and small circuits for formulas. J. Comput. Syst. Sci. 86, 136–158 (2017)

    Article  MathSciNet  Google Scholar 

  5. Lemay, A., Maneth, S., Niehren, J.: A learning algorithm for top-down XML transformations. In: Proceedings of PODS 2010, pp. 285–296. ACM (2010)

    Google Scholar 

  6. Lohrey, M., Maneth, S., Schmidt-Schauß, M.: Parameter reduction and automata evaluation for grammar-compressed trees. J. Comput. Syst. Sci. 78(5), 1651–1669 (2012)

    Article  MathSciNet  Google Scholar 

  7. Luttenberger, M., Palenta, R., Seidl, H.: Computing the longest common prefix of a context-free language in polynomial time. In: Proceedings of STACS 2018. LIPIcs, vol. 96, pp. 48:1–48:13. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)

    Google Scholar 

  8. Mohri, M.: Minimization algorithms for sequential transducers. Theor. Comput. Sci. 234(1–2), 177–201 (2000)

    Article  MathSciNet  Google Scholar 

  9. Oncina, J., García, P., Vidal, E.: Learning subsequential transducers for pattern recognition interpretation tasks. IEEE Trans. Pattern Anal. Mach. Intell. 15(5), 448–458 (1993)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. University of Siegen, Siegen, Germany

    Markus Lohrey

  2. University of Bremen, Bremen, Germany

    Sebastian Maneth

Authors
  1. Markus Lohrey
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  2. Sebastian Maneth
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Correspondence to Markus Lohrey .

Editor information

Editors and Affiliations

  1. University of Liverpool, Liverpool, UK

    Leszek Antoni Gąsieniec

  2. Hong Kong Polytechnic University, Hong Kong, China

    Jesper Jansson

  3. Lund University, Lund, Sweden

    Christos Levcopoulos

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Lohrey, M., Maneth, S. (2019). Largest Common Prefix of a Regular Tree Language. In: Gąsieniec, L., Jansson, J., Levcopoulos, C. (eds) Fundamentals of Computation Theory. FCT 2019. Lecture Notes in Computer Science(), vol 11651. Springer, Cham. https://doi.org/10.1007/978-3-030-25027-0_7

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  • DOI: https://doi.org/10.1007/978-3-030-25027-0_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-25026-3

  • Online ISBN: 978-3-030-25027-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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