Satisfiability of downward XPath with data equality tests

Figueira, Diego

doi:10.1145/1559795.1559827

Cited by 40 publications

(51 citation statements)

References 10 publications

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“…This settles a natural question left from the work in [13], also mentioned in [8,9]. As a consequence this also answers positively the open question raised in [1] on whether the downward fragment of XPath in the presence of DTDs is decidable.…”

Section: Introductionsupporting

confidence: 71%

“…1 In fact, we give a decision procedure for the satisfiability problem in the presence of any regular tree language, and we can therefore code the core of XML Schema (stripped of functional dependencies, except of unary primary keys) or Relax NG document types. 1 The same question on downward XPath but in the absence of DTDs was treated in [8].…”

Section: Introductionmentioning

confidence: 99%

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Forward-XPath and extended register automata on data-trees

Figueira

2010

Proceedings of the 13th International Conference on Database Theory

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We consider a fragment of XPath named 'forward-XPath', which contains all descendant and rightwards sibling axes as well as data equality and inequality tests. The satisfiability problem for forward-XPath in the presence of DTDs and even of primary key constraints is shown here to be decidable.To show decidability we introduce a model of alternating automata on data trees that can move downwards and rightwards in the tree, have one register for storing data and compare them for equality, and have the ability to (1) nondeterministically guess a data value and store it, and (2) quantify universally over the set of data values seen so far during the run. This model extends the work of Jurdziński and Lazić. Decidability of the finitary non-emptiness problem for this model is obtained by a direct reduction to a well-structured transition system, contrary to previous approaches.

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Section: Introductionsupporting

confidence: 71%

Section: Introductionmentioning

confidence: 99%

Forward-XPath and extended register automata on data-trees

Figueira

2010

Proceedings of the 13th International Conference on Database Theory

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“…Their XPath fragments support qualifier, union, and wildcard node test, but not parent, following-sibling, or precedingsibling axis. Figueira investigated satisfiability for XP {↓,↓ * ,=} without DTD and showed that the problem is EXPTIMEcomplete [6]. Ishihara et al proposed subclasses of covering DTDs and investigated the tractability of XPath satisfiability under the subclasses [7], [8].…”

Section: <!Element Students (Undergraduate|graduate)+>mentioning

confidence: 99%

Satisfiability of Simple XPath Fragments under Duplicate-Free DTDs

Suzuki

Fukushima²,

Ikeda

2013

IEICE Trans. Inf. & Syst.

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SUMMARYIn this paper, we consider the XPath satisfiability problem under restricted DTDs called "duplicate free". For an XPath expression q and a DTD D, q is satisfiable under D if there exists an XML document t such that t is valid against D and that the answer of q on t is nonempty. Evaluating an unsatisfiable XPath expression is meaningless, since such an expression can always be replaced by an empty set without evaluating it. However, it is shown that the XPath satisfiability problem is intractable for a large number of XPath fragments. In this paper, we consider simple XPath fragments under two restrictions: (i) only a label can be specified as a node test and (ii) operators such as qualifier ([ ]) and path union (∪) are not allowed. We first show that, for some small XPath fragments under the above restrictions, the satisfiability problem is NP-complete under DTDs without any restriction. Then we show that there exist XPath fragments, containing the above small fragments, for which the satisfiability problem is in PTIME under duplicate-free DTDs.

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“…Indeed, it can be seen that the TPQs with XPath-joins (i.e., the TPQs with joins satisfying the above condition) are precisely the TPQs with joins that can be expressed in downward navigational XPath with path equalities (as defined in [8]). 2 TPQs with XPath-joins are well-behaved in other respects as well.…”

Section: Definition 9 (Tree Pattern Queries With Joins)mentioning

confidence: 99%