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Deciding Twig-definability of Node Selecting Tree Automata

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Abstract

Node selecting tree automata (NSTAs) constitute a general formalism defining unary queries over trees. Basically, a node is selected by an NSTA when it is visited in a selecting state during an accepting run. We consider twig patterns as an abstraction of XPath. Since the queries definable by NSTAs form a strict superset of twig-definable queries, we study the complexity of the problem to decide whether the query by a given NSTA is twig-definable. In particular, we obtain that the latter problem is EXPTIME-complete. In addition, we show that it is also EXPTIME-complete to decide whether the query by a given NSTA is definable by a node selecting string automaton.

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Notes

  1. Filter is sometimes also called predicate, e.g., in the XPath specification by the World Wide Web Consortium.

  2. Recall that L a b e l s(r) is the set of symbols occurring in regular expressions r.

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Authors and Affiliations

  1. Hasselt University and Transnational University of Limburg, Hasselt, Belgium

    Timos Antonopoulos & Frank Neven

  2. University of Oslo, Oslo, Norway

    Dag Hovland

  3. Universität Bayreuth, Bayreuth, Germany

    Wim Martens

Authors
  1. Timos Antonopoulos
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  2. Dag Hovland
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  3. Wim Martens
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  4. Frank Neven
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Corresponding author

Correspondence to Dag Hovland.

Additional information

An extended abstract of this paper appeared in [2]

We acknowledge the financial support of the Future and Emerging Technologies (FET) programme within the Seventh Framework Programme for Research of the European Commission, under the FET-Open grant agreement FOX, number FP7-ICT-233599.

Supported by grant number MA 4938/2–1 from the Deutsche Forschungsgemeinschaft (Emmy Noether Nachwuchsgruppe).

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Antonopoulos, T., Hovland, D., Martens, W. et al. Deciding Twig-definability of Node Selecting Tree Automata. Theory Comput Syst 57, 967–1007 (2015). https://doi.org/10.1007/s00224-015-9623-7

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  • DOI: https://doi.org/10.1007/s00224-015-9623-7

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