Extending two-variable logic on data trees with order on data values and its automata.
Journal
ACM Transactions on Computational Logic
Journal Volume
15
Journal Issue
1
Date Issued
2014
Author(s)
TONY TAN
Abstract
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 complexity of the non-emptiness problem drops to NP. However, a number of existing formalisms and models studied in the literature can be captured already by weak ODTA. We also show that the definition of ODTA can be easily modified, to the case where the data values come from a tree-like partially ordered domain, such as strings. © 2014 ACM.
Subjects
Data trees; Finite-state automata; Ordered data values; Two-variable logic
Other Subjects
Abstraction model; Automata models; Data tree; Finite alphabet; Finite-state automata; Infinite domains; Ordered data; Two-variable logic; Automata theory; Forestry; Trees (mathematics); Algorithms; Data Bases; Mathematical Models; Problem Solving
Type
journal article