G. J. Bex, S. Maneth, and F. Neven. A formal model for an expressive fragment of XSLT. Information Systems, 28(1):21--39, 2002.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....the logics provided by its DSD and (d) the representation of the proof like the one described above. Of these elements, the only missing one is the representation of the semantics of XSLT. There are several attempts, however, to provide a semantics for XSLT fragments that can be used [Wadler 2000, Bex 2000] Another path, consists of defining a transformation language simpler than XSLT but with a clean semantics. This is partly the case of Transmorpher (see 5) Checking is the opposite of trusting. Both approaches have different advantages: trusting does not require to spend time checking the ....

Geert Jan Bex, Sebastian Maneth, Frank Neveu, A formal model for an expressive fragment of XSLT, Lecture notes in computer science 1861:1137-1151, 2000

....of element nodes within XML documents. It has been widely used in XML query languages (e.g. XSLT [7] XQL [22] XQuery [5] XML specifications (e.g. XML Schema [23] and subscription systems (e.g. 6] It supports a number of powerful modalities and thus is rather expensive to process [3, 18, 10]. In practice, many applications do not need the excessive power of the full language; they use only a fragment of XPath. For example, XML Schema specifies integrity constraints with an XPath fragment that does not support upward modalities (the parent and ancestor axes) It is thus necessary to ....

....of expressions. Taken together, these results give a picture of the advantages and disadvantages of working within a particular fragment. Related work: There has been considerable work on the expressiveness and complexity of XPath. One line of investigation studies formal models of XPath [3, 18, 17, 16], abstracting away from the concrete syntax of XPath into a powerful automaton model complexity bounds are then derived from bounds on the automata. The results to date have generally given considerable insight into the expressiveness and complexity of XPath as a whole, but have shed little ....

G. Bex, S. Maneth, and F. Neven. A formal model for an expressive fragment of XSLT. Information Systems, 27(1):21- 39, 2002.

.... to the size of the XML data and the growing size and intricacy of the queries (usually referred to as combined complexity) Recently, there has been some work on related problems such as query containment for XPath [5, 11, 16] the expressiveness and complexity of various fragments of XSLT [2, 12], and contributions towards a formal semantics definition of XPath [6, 14] However, to the best of our knowledge, no research results on good or even reasonable methods for processing XPath have been published which may serve as yardsticks for new algorithms. # This work was supported by the ....

G. J. Bex, S. Maneth, and F. Neven. A Formal Model for an Expressive Fragment of XSLT. In Proc. CL 2000.

....a formal semantics definition of XPath [9, 16, 10] Moreover, the expressiveness # This work was supported by the Austrian Science Fund (FWF) under project No. Z29 INF. All methods and algorithms presented in this paper are covered by a pending patent. and complexity of various fragments of XSLT [3, 14, 2] and XML query pattern matching [15, 4, 6] have been investigated. However, only very recently, the first polynomialtime algorithm for evaluating arbitrary XPath 1.0 queries has been published (cf. 11] In contrast, experiments with three existing XPath processors (namely XALAN [19] XT [7] ....

G. J. Bex, S. Maneth, and F. Neven. A Formal Model for an Expressive Fragment of XSLT. In Proc. CL 2000.

....are two main problems when translating XSL stylesheets into an algebraic expression. The first one is the template selection process. This process has been discussed in the previous section. The second problem occurs with xsl:apply templates instructions. These imply recursion of high complexity [5]. In principle, there should be two solutions to the problem: using a fixpoint operator as in Datalog [22] or using a stack to resolve recursion. We decided to take the second approach since order preserving fixpoint operations which are also efficient are not known to us. Maybe future research ....

....GPush then looks at the top of the stack, recognizes itself in the resumeOp attribute and hands the tuple upwards. Note that a plan may never halt. This is due to the fact that stylesheet processing itself may also not terminate. The problem to determine whether it halts or not is undecidable [5]. 5 Optimizing the Initial Plan Every node processed by a stylesheet enters the stylesheet s core plan at the Distributor. Except for the root node, GPush sends the nodes to the Distributor via the stack. The main idea of the optimization process is to successively replace GPush operations by ....

G. Bex, S. Maneth, and F. Neven. A formal model for an expressive fragment of XSLT. Computational Logic, pages 1137--1151, 2000.

....problem is polynomial. Related Work Based on a wealth of elegant equivalences between regular tree languages, logics (MSO) and automata (cf. 28, 29, 6] there has recently been considerable research activity related to various theoretical aspects of XPath and XSLTlike query languages [25, 7, 5, 22, 24, 16]. However, except for [17] which shows that XPath has polynomial time combined complexity, and the linear time combined complexity result for monadic datalog over trees of [16] no research results on good or even reasonable algorithms for processing XPath and similar languages have been ....

G. J. Bex, S. Maneth, and F. Neven. A Formal Model for an Expressive Fragment of XSLT. In CL 2000.

.... intricacy of the queries (usually referred to as combined complexity) Recently, there has been some work on related problems such as query containment for XPath [6, 11, 16] XPath axis rewriting to deal with streaming XML data [4] the expressiveness and complexity of various fragments of XSLT [2, 12], and contributions towards a # This work was supported by the Austrian Science Fund (FWF) under project No. Z29 INF. All methods and algorithms presented in this paper are covered by a pending patent. Further resources, updates, and possible corrections will be made available at ....

G. J. Bex, S. Maneth, and F. Neven. A Formal Model for an Expressive Fragment of XSLT. In Proc. CL 2000.

....logics provided by their DSD and (d) the representation of the proof like the one described above. Of these elements, the only missing one is the representation of the semantics of XSLT. There are several attempts, however, to provide a semantics for XSLT fragments that can be used [Wadler 2000, Bex 2000] Another path consists of defining a transformation language simpler than XSLT but with a clean semantics. This is partly the case of Transmorpher. Checking is the opposite of trusting. Both approaches have different advantages: trusting does not require to spend time checking the arguments ....

Geert Jan Bex, Sebastian Maneth, Frank Neveu, A formal model for an expressive fragment of XSLT, Lecture notes in computer science 1861:1137-1151, 2000

....of pattern languages based on regular path expressions, a guarded fragment of MSO that is equivalent to MSO but that can be evaluated much more efficiently is studied in [86, 96] For example, it is shown that this fragment of MSO can express FO extended with regular path expressions. In [18] a formal model for XSLT is defined incorporating features like modes, variables, and parameter passing. Although this model is not computational complete, it can simulate k pebble transducers, even extended with equality tests on data values. Consequently, and contrary to conventional wisdom, ....

G. Bex, S. Maneth, and F. Neven. A formal model for an expressive fragment of XSLT. In Proc. DOOD, pages 1137--1151, 2000.

....could not express data value joins and its expressive power for tree transformations was strictly less than that of k pebble transducers. Recent additions to the language however include data value joins and constructs made it at least as expressive as k pebble transducers for tree transformations [6]. An analysis of the expressive power of the entire language has to wait until the language stabilizes. The second limitation is the complexity. A direct application of our method for typechecking k pebble transducers results in complexity hyperexponential in k (so nonelementary) due to a ....

G. J. Bex, S. Maneth, and F. Neven. A formal model for an expressive fragment of XSLT, 2000. manuscript.

.... recognize regular languages only [15] and this also holds when generalized to trees [8] Even more recently, a corresponding tree transducer model was proposed as a general model for XML based query languages: the so called pebble tree transducer [20, 28] related models are considered in, e.g. [1, 21, 22]) Here we study some theoretical properties of the pebble tree transducer of [20, 28] restricted to monadic trees, i.e. to strings: the two way nite state transducer with nested pebbles (pebble transducer, for short) For a string w, jwj denotes its length, and w(i) denotes its ith element. The ....

G. J. Bex, S. Maneth, F. Neven; A formal model for an expressive fragment of XSLT, Information Systems 27 (2002), 21-39

....Since XML documents have a tree structure (usually defined by DTDs) XML queries can be modeled as mappings from trees to trees (tree transductions) and schema languages are closely related to tree automata. Therefore automata theory has naturally emerged as a central tool in formal work on XML [6, 18, 19, 20, 21, 22, 23, 24]. The connection to logic and automata proved very fruitful in understanding such languages and in the development of optimization algorithms and static analysis techniques. However, these abstractions ignore an important aspect of XML, namely the presence of data values attached to leaves of ....

G. J. Bex, S. Maneth, and F. Neven. A formal model for an expressive fragment of XSLT. Information Systems, 27(1):21--39, 2002.

.... recognize regular languages only [15] and this also holds when generalized to trees [8] Even more recently, a corresponding tree trans ducer model was proposed as a general model for XML based query languages: the so called pebble tree transducer [20,28] related models are considered in, e.g. [1,21,22]) Here we study some theoretical properties of the pebble tree transducer of [20,28] restricted to monadic trees, i.e. to strings: the two way finite state transducer with nested pebbles (pebble transducer, for short) For a string w, w[ denotes its length, and w(i) denotes its ith element. ....

G. J. Bex, S. Maneth, F. Neven; A formal model for an expressive fragment of XSLT, Information Systems 27 (2002), 21-39

.... research on compilers and attribute grammars [1, 6] Tree walking automata are still considered in formal language theory as the connection with tree automata is still unknown [7, 8, 25] In the context of XML, the tree walking paradigm attracted attention as an abstraction of XML query languages [2, 17, 23] and streaming [33] Infinite alphabets. The framework considered in this paper is limited in two ways. It assumes that the element names of XML documents are from a finite and known set and it ignores the data values in the leaf nodes and attributes of XML documents. For this reason, the work of ....

G. J. Bex, S. Maneth, and F. Neven. A formal model for an expressive fragment of XSLT. Information Systems, 27(1):21--39, 2002.

....1 Introduction XPath is a simple language for navigating an XML document and selecting a set of element nodes [6] Actually, XPath is the main XML selection language. Indeed, XPath expressions are used, for instance, as basic patterns in several XML query languages like XQuery [3] and XSLT [2, 7]; they are used in XML Schema to define keys [8] and in XLink [10] and XPointer [9] to reference elements in external documents. In every such context an instance of the containment problem is present: optimizing XPath expressions can be accomplished by an algorithm for containment, and XSLT rule ....

....When # and A are clear from the context or not important, we sometimes say tree rather than (#, A) tree. Of course, in real XML documents not every element has the same attributes. Further, there can be nodes with mixed content, but these can easily be modeled by using dummy intermediate nodes [2]. We only make use of attributes in Section 5. We formalize a DTD as a context free grammar with regular expressions on the right hand side of rules. Definition 2. A DTD is a tuple (d, S d , # d ) where # d is a finite subset of #, # d is the start symbol, and d is a mapping from # d to the ....

G. J. Bex, S. Maneth, and F. Neven. A formal model for an expressive fragment of XSLT. Information Systems, 27(1):21--39, 2002.

....a rst instance of tree walking is provided by the caterpillar expressions of Br uggemann Klein and Wood [7] Further, Milo, Suciu, and Vianu [17] de ned a tree walking tree transducer model with pebbles as an abstract model for XML transformations. Finally, as argued by Bex, Maneth and Neven [4], stripped down, XSLT is essentially a tree walking tree transducer with registers and look ahead. The present investigation is motivated by the latter model. In brief, registers deal with data values and look ahead allows sub computations. As we focus on the computational aspect of tree walking, ....

....of tree walking devices as they work directly on trees. Further, there is a natural time space correspondence with ordinary Turing machines working on encodings of attributed trees. When no attributes are present, it is easy to see that relational storage does not add additional power. In [4] it is shown that adding look ahead allows to capture all unary monadic second order logic formulas (MSO) and, therefore, all regular tree languages [18] Hence, whether look ahead adds power depends on the open question whether treewalking captures all regular tree languages [12, 13, 19] This ....

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G. J. Bex, S. Maneth and F. Neven. A formal model for an expressive fragment of XSLT. Information Systems, 27(1): 21-39, 2002.

....general exptime exptime exptime exptime exptime non deleting exptime exptime pspace pspace conp bounded width exptime in exptime pspace hard pspace ptime conp on unranked trees. Such transformations correspond to structural recursion on trees [5] and to simple top down XSLT transformations [3, 6]. The transducers are called uniform as they cannot distinguish between the order of siblings. In brief, a transformation consists of a top down traversal of the input tree where every node is replaced by a new tree (possibly the empty tree) We show that the ability of transducers to delete ....

G. J. Bex, S. Maneth, and F. Neven. A formal model for an expressive fragment of XSLT. Information Systems, 27(1):21--39, 2002.

....and Wood [9] Further, Milo, Suciu, and Vianu [34] defined a tree walking tree transducer model with pebbles as an abstract model for XML transformations. Segoufin and Vianu considered treewalking automata in the context of XML streaming [51] Finally, as argued by Bex, Maneth and Neven [6], stripped down, XSLT is essentially a tree walking tree transducer with registers and look ahead. We embark on the issue of registers and look ahead in the next section. In the present section, we consider ordinary tree walking automata. Admittedly, the application of tree walking to XML is ....

....finite model theory, and formal languages, they provide a quite complete picture of the expressiveness of query languages based on tree walking. The most surprising might be that DTWAs extended with single valued registers and subcomputations, which is the abstraction of XSLT defined in [6], captures in fact precisely ptime. 7 Discussion We considered three automata models that regained interest by the advent of XML. Our main focus was on their connection with logic and on questions motivated by XML. We hope to have convinced the reader that XML poses new challenges on the ....

G. J. Bex, S. Maneth, and F. Neven. A formal model for an expressive fragment of XSLT. Information Systems, 27(1):21--39, 2002.

....encompassing most current XML transformation languages. Another occurrence of tree walking automata is embodied in the actual XML transformation language XSLT [7] proposed by the W3C. In formal language theoretic terms, this query language can be best described as a tree walking tree transducer [2]. As a third example we mention the caterpillar expressions of BruggemanKlein and Wood. 5] These are regular expressions over moving instructions up, left, down, right, isLeaf, isFirst, isLast, isRoot and # symbols. For instance, 11 the expression a isLeaf (up # b down # c) selects all ....

....strings of the same form u#v as before. Define N u and N v as the set of symbols occurring in attributes in u and v, respectively. It can be shown that there is a register automaton that accepts u#v i# N u = N v while there is no such MSO sentence. The formal model of XSLT of [2] is based on tree walking transducers with registers. By applying Theorem 13 we get that XSLT programs without nested calls cannot define all of FO. Pebble automata behave much better, their expressiveness lies in between FO and MSO. Indeed, pebbles provide a mechanism to instantiate variables ....

G. J. Bex, S. Maneth, and F. Neven. A formal model for an expressive fragment of XSLT. 1st International Conference on Computational Logic, pages 1137--1151, Lecture Notes in Artificial Intelligence, volume 1861. Springer, 2000.

.... Web [1] Since XML documents have a tree structure (usually defined by DTDs) XML queries can be modeled as mappings from trees to trees (tree transductions) and schema languages are closely related to tree automata, automata theory has naturally emerged as a central tool in formal work on XML [5, 17, 18, 19, 20, 21, 22, 23]. The connection to logic and automata proved very fruitful in understanding such languages and in the development of optimization algorithms and static analysis techniques. However, these abstractions ignore an important aspect of XML, namely the presence of data values attached to leaves of ....

G. J. Bex, S. Maneth, and F. Neven. A formal model for an expressive fragment of XSLT. In Lloyd et al., editor, Computational Logic -- CL

.... the Web [1] Since XML documents have a tree structure (usually de ned by DTDs) XML queries can be modeled as mappings from trees to trees (tree transductions) and schema languages are closely related to tree automata, automata theory has naturally emerged as a central tool in formal work on XML [5, 16 22]. The connection to logic and automata proved very fruitful in understanding such languages and in the development of optimization algorithms and static analysis techniques. However, these abstractions ignore an important aspect of XML, namely the presence of data values attached to leaves of ....

G. J. Bex, S. Maneth, and F. Neven. A formal model for an expressive fragment of XSLT. In Lloyd et al., editor, Computational Logic { CL 2000, volume 1861 of Lecture Notes in Articial Intelligence, pages 1137-1151. Springer, 2000.

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G. J. Bex, S. Maneth, and F. Neven. A formal model for an expressive fragment of XSLT. Information Systems, 28(1):21--39, 2002.

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Geert Jan Bex, Sebastian Maneth, and Frank Neven. A formal model for an expressive fragment of XSLT. Information Systems, 27(1):21--39, 2002.

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G. J. Bex, S. Maneth, and F. Neven. A formal model for an expressive fragment of XSLT. Information Systems, 27(1):2139, 2002.

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G. J. Bex, S. Maneth, and F. Neven. A formal model for an expressive fragment of XSLT. In L. et al., editor, Computational Logic { CL 2000.

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