Z-Automata for Compact and Direct Representation of Unranked Tree Languages

  • Johanna Björklund
  • Frank DrewesEmail author
  • Giorgio Satta
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11601)


Unranked tree languages are valuable in natural language processing for modelling dependency trees. We introduce a new type of automaton for unranked tree languages, called Z-automaton, that is tailored for this particular application. The Z-automaton offers a compact form of representation, and unlike the closely related notion of stepwise automata, does not require a binary encoding of its input. We establish an arc-factored normal form, and prove the membership problem of Z-automata in normal form to be in \( O \left( mn \right) \), where m is the size of the transition table of the Z-automaton and n is the size of the input tree.



We thank the reviewers for carefully reading the manuscript. In particular, we thank one reviewer who pointed out a flaw in the original version of Theorem 1.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Johanna Björklund
    • 1
  • Frank Drewes
    • 1
    Email author
  • Giorgio Satta
    • 2
  1. 1.Department of Computing ScienceUmeå UniversityUmeåSweden
  2. 2.Department of Information EngineeringUniversity of PaduaPaduaItaly

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