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Decidability of Downward XPath

Decidability of Downward XPath Decidability of Downward XPath DIEGO FIGUEIRA, INRIA, ENS Cachan, LSV and University of Edinburgh We investigate the satisfiability problem for downward-XPath, the fragment of XPath that includes the child and descendant axes, and tests for (in)equality of attributes' values. We prove that this problem is decidable, E XP T IME-complete. These bounds also hold when path expressions allow closure under the Kleene star operator. To obtain these results, we introduce a Downward Data automata model (DD automata) over trees with data, which has a decidable emptiness problem. Satisfiability of downward-XPath can be reduced to the emptiness problem of DD automata and hence its decidability follows. Although downward-XPath does not include any horizontal axis, DD automata are more expressive and can perform some horizontal tests. Thus, we show that the satisfiability remains in E XP T IME even in the presence of the regular constraints expressible by DD automata. However, the same problem in the presence of any regular constraint is known to have a nonprimitive recursive complexity. Finally, we give the exact complexity of the satisfiability problem for several fragments of downward-XPath. Categories and Subject Descriptors: I.7.2 [Document Preparation]: Markup Languages; H.2.3 [Database Management]: Languages; H.2.3 [Languages]: Query http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Computational Logic (TOCL) Association for Computing Machinery

Decidability of Downward XPath

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References (27)

Publisher
Association for Computing Machinery
Copyright
Copyright © 2012 by ACM Inc.
ISSN
1529-3785
DOI
10.1145/2362355.2362362
Publisher site
See Article on Publisher Site

Abstract

Decidability of Downward XPath DIEGO FIGUEIRA, INRIA, ENS Cachan, LSV and University of Edinburgh We investigate the satisfiability problem for downward-XPath, the fragment of XPath that includes the child and descendant axes, and tests for (in)equality of attributes' values. We prove that this problem is decidable, E XP T IME-complete. These bounds also hold when path expressions allow closure under the Kleene star operator. To obtain these results, we introduce a Downward Data automata model (DD automata) over trees with data, which has a decidable emptiness problem. Satisfiability of downward-XPath can be reduced to the emptiness problem of DD automata and hence its decidability follows. Although downward-XPath does not include any horizontal axis, DD automata are more expressive and can perform some horizontal tests. Thus, we show that the satisfiability remains in E XP T IME even in the presence of the regular constraints expressible by DD automata. However, the same problem in the presence of any regular constraint is known to have a nonprimitive recursive complexity. Finally, we give the exact complexity of the satisfiability problem for several fragments of downward-XPath. Categories and Subject Descriptors: I.7.2 [Document Preparation]: Markup Languages; H.2.3 [Database Management]: Languages; H.2.3 [Languages]: Query

Journal

ACM Transactions on Computational Logic (TOCL) – Association for Computing Machinery

Published: Oct 1, 2012

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