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XPath, transitive closure logic, and nested tree walking automata

Published:09 June 2008Publication History

ABSTRACT

We consider the navigational core of XPath, extended with two operators: the Kleene star for taking the transitive closure of path expressions, and a subtree relativisation operator, allowing one to restrict attention to a specific subtree while evaluating a subexpression. We show that the expressive power of this XPath dialect equals that of FO(MTC), first order logic extended with monadic transitive closure. We also give a characterization in terms of nested tree-walking automata. Using the latter we then proceed to show that the language is strictly less expressive than MSO. This solves an open question about the relative expressive power of FO(MTC) and MSO on trees. We also investigate the complexity for our XPath dialect. We show that query evaluation be done in polynomial time (combined complexity), but that satisfiability and query containment (as well as emptiness for our automaton model) are 2ExpTime-complete (it is ExpTime-complete for Core XPath).

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    • Published in

      cover image ACM Conferences
      PODS '08: Proceedings of the twenty-seventh ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
      June 2008
      330 pages
      ISBN:9781605581521
      DOI:10.1145/1376916

      Copyright © 2008 ACM

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      Association for Computing Machinery

      New York, NY, United States

      Publication History

      • Published: 9 June 2008

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