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Satisfiability of XPath Expressions [chapter]

Jan Hidders
2004 Lecture Notes in Computer Science  
In this paper, we investigate the complexity of deciding the satisfiability of XPath 2.0 expressions, i.e., whether there is an XML document for which their result is nonempty.  ...  Several fragments that allow certain types of expressions are classified as either in PTIME or NP-hard to see which type of expression make this a hard problem.  ...  Finally, we define what it means for an XPath expression to be satisfiable.  ... 
doi:10.1007/978-3-540-24607-7_3 fatcat:ornsvteug5hqppafpqklk57hqu

Comparing XML path expressions

Pierre Genevès, Nabil Layaïda
2006 Proceedings of the 2006 ACM symposium on Document engineering - DocEng '06  
We present a translation of a large XPath fragment into µcalculus, together with practical experiments on the containment using a state-of-the-art EXPTIME decision procedure for µ-calculus satisfiability  ...  XPath decision problems have attracted a lot of research attention, especially for studying the computational complexity of various XPath fragments.  ...  Logical Translation of Expressions The translation of XPath expressions into µ-calculus is given on Figure 8 .  ... 
doi:10.1145/1166160.1166182 dblp:conf/doceng/GenevesL06 fatcat:dwsttxhcpvccxg2v6y44kxojga

Satisfiability of XPath Queries with Sibling Axes [chapter]

Floris Geerts, Wenfei Fan
2005 Lecture Notes in Computer Science  
To this end we revisit the satisfiability problem for a variety of XPath fragments with sibling axes, in the presence of DTDs, in the absence of DTDs, and under various restricted DTDs.  ...  Although this problem was recently studied for XPath fragments without sibling axes, little is known about the impact of the sibling axes on the satisfiability analysis.  ...  Floris Geerts is postdoctoral researcher of the FWO Vlaanderen and is supported in part by EPSRC GR/S63205/01.  ... 
doi:10.1007/11601524_8 fatcat:4djmfhwayrb5bjflo4ugxmmyz4

A system for the static analysis of XPath

Pierre Genevès, Nabil Layaïda
2006 ACM Transactions on Information Systems  
We present a sound and complete decision procedure for containment of XPath queries as well as other related XPath decision problems such as satisfiability, equivalence, overlap and coverage.  ...  Based on these embeddings, we show how XPath decision problems, in the presence or the absence of XML types, can be solved using a decision procedure for µ-calculus satisfiability.  ...  XPath Expressions used in the presence of DTDs.  ... 
doi:10.1145/1185877.1185882 fatcat:vkewxlmspzcivoxpnyy7itlftq

Equipping IDEs with XML-Path Reasoning Capabilities

Pierre Genevès, Nabil Layaïda
2014 ACM Transactions on Internet Technology  
We present the first IDE augmented with static detection of inconsistent XPath expressions that assists the programmer for simplifying the development and debugging of any application involving XPath expressions  ...  The tool is based on newly developed formal verification techniques based on expressive modal logics, which are now mature enough to be introduced in the process of software development.  ...  One of the most basic rules consists in replacing an inconsistent XPath expression by the empty node sequence, as follows: ¬satisfiable(path, S) S, Γ : path −→ () where the predicate satisfiable(path,  ... 
doi:10.1145/2602573 fatcat:pdef2e2cqbablmnobiys4o7kti

XML Static Analyzer User Manual [article]

Pierre Geneves, Nabil Layaida
2008 arXiv   pre-print
Logical formulas can be expressed using the syntax of XPath expressions, DTD, XML Schemas, and Relax NG definitions.  ...  The solver allows automated verification of properties that are expressed as logical formulas over trees.  ...  In that case, the formula is satisfiable (the XPath expression is non-empty in the presence of this DTD). The solver outputs a sample tree for which the formulas is satisfied.  ... 
arXiv:0812.3550v1 fatcat:fbritpe7nzefbktz5zovi2xuoq

XPath satisfiability in the presence of DTDs

Michael Benedikt, Wenfei Fan, Floris Geerts
2008 Journal of the ACM  
We study the satisfiability problem associated with XPath in the presence of DTDs.  ...  We consider a variety of XPath fragments widely used in practice, and investigate the impact of different XPath operators on satisfiability analysis.  ...  Floris Geerts is postdoctoral researcher of the FWO Vlaanderen and is supported in part by EPSRC GR/S63205/01.  ... 
doi:10.1145/1346330.1346333 fatcat:rpp2yr4k7rfhxaixxbt3rn6bdi

XPath satisfiability in the presence of DTDs

Michael Benedikt, Wenfei Fan, Floris Geerts
2005 Proceedings of the twenty-fourth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems - PODS '05  
We study the satisfiability problem associated with XPath in the presence of DTDs.  ...  We consider a variety of XPath fragments widely used in practice, and investigate the impact of different XPath operators on satisfiability analysis.  ...  Floris Geerts is postdoctoral researcher of the FWO Vlaanderen and is supported in part by EPSRC GR/S63205/01.  ... 
doi:10.1145/1065167.1065172 dblp:conf/pods/BenediktFG05 fatcat:orcljera6fcotfh5tu37rq45xa

Static analysis of XML processing with data values

Luc Segoufin
2007 SIGMOD record  
Open problem 1 Is satisfiability of FO 2 (∼, <, +1) decidable over data trees?  ...  We thank Michael Benedikt, Leonid Libkin and Thomas Schwentick for all their comments on an earlier version of this paper.  ...  The following expression is also safe: Child :: b/@B 1 = Self :: a/@B 2 . Theorem 6 [5] Satisfiability and containment for XPath-local safe expressions is decidable.  ... 
doi:10.1145/1276301.1276308 fatcat:a6kzyaipprcybcx6wmod4tcyfu

On the analysis of queries with counting constraints

Everardo Bárcenas, Pierre Genevès, Nabil Layaïda
2009 Proceedings of the 9th ACM symposium on Document engineering - DocEng '09  
We study the analysis problem of XPath expressions with counting constraints.  ...  We explore how recent results on the static analysis of navigational aspects of XPath can be extended to counting constraints.  ...  In Section 3, by means of a linear translation of XPath expressions into the logic, we identify a decidable fragment of the XPath language where cardinality constraints are allowed.  ... 
doi:10.1145/1600193.1600199 dblp:conf/doceng/BarcenasGL09 fatcat:jhfjr7ezxzcs5lkdcyl6lljz7m

XPath Satisfiability with Parent Axes or Qualifiers Is Tractable under Many of Real-World DTDs [article]

Yasunori Ishihara, Nobutaka Suzuki, Kenji Hashimoto, Shogo Shimizu, Toru Fujiwara
2013 arXiv   pre-print
This paper aims at finding a subclass of DTDs that covers many of the real-world DTDs while offering a polynomial-time complexity for deciding the XPath satisfiability problem.  ...  However, under RW-DTDs, XPath satisfiability with only child, descendant-or-self, and sibling axes is tractable.  ...  This research is supported in part by Grant-in-Aid for Scientific Research (C) 23500120 from Japan Society for the Promotion of Science.  ... 
arXiv:1308.0769v1 fatcat:t3pe4rzlenc4ndmemobjopkw2q

Definability for Downward and Vertical XPath on Data Trees [chapter]

Sergio Abriola, María Emilia Descotte, Santiago Figueira
2014 Lecture Notes in Computer Science  
We study the expressive power of the downward and vertical fragments of XPath equipped with (in)equality tests over data trees.  ...  We give necessary and sufficient conditions for a class of pointed data trees to be definable by a set of formulas or by a single formula of each of the studied logics.  ...  An XPath = -formula [resp. XPath ↓ =formula] is simply a node expression of XPath = [resp. XPath ↓ = ].  ... 
doi:10.1007/978-3-662-44145-9_2 fatcat:m4rg3xu2hvg73pezaeqx5bk4bm

Structural characterizations of the semantics of XPath as navigation tool on a document

Marc Gyssens, Jan Paredaens, Dirk Van Gucht, George H. L. Fletcher
2006 Proceedings of the twenty-fifth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems - PODS '06  
In this view, we characterize when a set of nodes in D can be defined as the result of applying an XPath expression to a given node of D.  ...  Given a document D in the form of an unordered labeled tree, we study the expressibility on D of various fragments of XPath, the core navigational language on XML documents.  ...  Since downward 3-equivalence is the coarsest equivalence relation satisfying conditions (1), (2), and (3) of Definition 8, it suffices to prove that expression equivalence satisfies these conditions.  ... 
doi:10.1145/1142351.1142397 dblp:conf/pods/GyssensPGF06 fatcat:foci2wxbozf6phvlomwpj7giyy

Axiomatizing the Logical Core of XPath 2.0

Balder ten Cate, Maarten Marx
2008 Theory of Computing Systems  
The first aim of this paper is to present the logical core of XPath 2.0: a logically clean, decidable fragment, which includes most navigational features of XPath 2.0 (complex counting conditions and data  ...  The second aim is to provide a list of equations completely axiomatizing query equivalence in this language (i.e., all other query equivalences can be derived from these).  ...  It follows by Theorem 4 that every first-order formula, and therefore also every Core XPath 2.0 expression, satisfied in M is satisfied in some finite tree.  ... 
doi:10.1007/s00224-008-9151-9 fatcat:6wgsuynzfzclff3vddic5t5uui

Decidable XPath Fragments in the Real World

David Baelde, Anthony Lick, Sylvain Schmitz
2019 Proceedings of the 38th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems - PODS '19  
Besides query evaluation, query satisfiability and containment are the main computational problems for XPath; they are useful, for instance, to detect dead code or validate query optimisations.  ...  To investigate the practical impact of these theoretical fragments, we design a benchmark compiling thousands of real-world XPath queries extracted from open-source projects.  ...  Figure 4 : 4 The semantics of XPath axes. with XPath 3.0: all the examples in this paper are written in actual XPath. Figure 5 : 5 The semantics of XPath path expressions and node expressions.  ... 
doi:10.1145/3294052.3319685 dblp:conf/pods/BaeldeLS19 fatcat:p5ltcdprgngsld3ueyiyybxhwy
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