On the power of walking for querying tree-structured data

  • Authors:

  • Frank Neven

  • Affiliations:

  • University of Limburg

  • Venue:
  • Proceedings of the twenty-first ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
  • Year:
  • 2002

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Abstract

XSLT is the prime example of an XML query language based on tree-walking. Indeed, stripped down, XSLT is just a tree-walking tree-transducer equipped with registers and look-ahead. Motivated by this connection, we want to pinpoint the computational power of devices based on tree-walking. We show that in the absence of unique identifiers even very powerful extensions of the tree-walking paradigm are not relationally complete. That is, these extensions do not capture all of first-order logic. In contrast, when unique identifiers are available, we show that various restrictions allow to capture LOGSPACE, PTIME, PSPACE, and EXPTIME. These complexity classes are defined w.r.t. a Turing machine model working directly on (attributed) trees. When no attributes are present, relational storage does not add power; whether look-ahead adds power is related to the open question whether tree-walking captures the regular tree languages.