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Extending two-variable logic on data trees with order on data values and its automata

Extending two-variable logic on data trees with order on data values and its automata Extending Two-Variable Logic on Data Trees with Order on Data Values and Its Automata TONY TAN, Hasselt University and Transnational University of Limburg Data trees are trees in which each node, besides carrying a label from a finite alphabet, also carries a data value from an infinite domain. They have been used as an abstraction model for reasoning tasks on XML and verification. However, most existing approaches consider the case where only equality test can be performed on the data values. In this article we study data trees in which the data values come from a linearly ordered domain, and in addition to equality test, we can test whether the data value in a node is greater than the one in another node. We introduce an automata model for them which we call ordered-data tree automata (ODTA), provide its logical characterisation, and prove that its non-emptiness problem is decidable in 3-NEXPTIME. We also show that the two-variable logic on unranked data trees, studied by Bojanczyk et al. [2009], corresponds precisely to a special subclass of this automata model. Then we define a slightly weaker version of ODTA, which we call weak ODTA, and provide its logical characterisation. The http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Computational Logic (TOCL) Association for Computing Machinery

Extending two-variable logic on data trees with order on data values and its automata

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References (44)

Publisher
Association for Computing Machinery
Copyright
Copyright © 2014 by ACM Inc.
ISSN
1529-3785
DOI
10.1145/2559945
Publisher site
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Abstract

Extending Two-Variable Logic on Data Trees with Order on Data Values and Its Automata TONY TAN, Hasselt University and Transnational University of Limburg Data trees are trees in which each node, besides carrying a label from a finite alphabet, also carries a data value from an infinite domain. They have been used as an abstraction model for reasoning tasks on XML and verification. However, most existing approaches consider the case where only equality test can be performed on the data values. In this article we study data trees in which the data values come from a linearly ordered domain, and in addition to equality test, we can test whether the data value in a node is greater than the one in another node. We introduce an automata model for them which we call ordered-data tree automata (ODTA), provide its logical characterisation, and prove that its non-emptiness problem is decidable in 3-NEXPTIME. We also show that the two-variable logic on unranked data trees, studied by Bojanczyk et al. [2009], corresponds precisely to a special subclass of this automata model. Then we define a slightly weaker version of ODTA, which we call weak ODTA, and provide its logical characterisation. The

Journal

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

Published: Feb 1, 2014

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