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31
Frontiers of tractability for typechecking simple XML transformations
 PODS
, 2004
"... Typechecking consists of statically verifying whether the output of an XML transformation is always conform to an output type for documents satisfying a given input type. We focus on complete algorithms which always produce the correct answer. We consider topdown XML transformations incorporating X ..."
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Cited by 33 (6 self)
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Typechecking consists of statically verifying whether the output of an XML transformation is always conform to an output type for documents satisfying a given input type. We focus on complete algorithms which always produce the correct answer. We consider topdown XML transformations incorporating XPath expressions and abstract document types by grammars and tree automata. By restricting schema languages and transformations, we identify several practical settings for which typechecking is in polynomial time. Moreover, the resulting framework provides a rather complete picture as we show that most scenarios can not be enlarged without rendering the typechecking problem intractable. So, the present research sheds light on when to use fast complete algorithms and when to reside to sound but incomplete ones.
Counting in Trees for Free
, 2004
"... In [22], it was shown that MSO logic for ordered unranked trees becomes undecidable if Presburger constraints are allowed at children of nodes. We now show that a decidable logic is obtained if we use a a modal fixpoint logic instead. We present an automata theoretic characterization of this logi ..."
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Cited by 28 (1 self)
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In [22], it was shown that MSO logic for ordered unranked trees becomes undecidable if Presburger constraints are allowed at children of nodes. We now show that a decidable logic is obtained if we use a a modal fixpoint logic instead. We present an automata theoretic characterization of this logic by means of deterministic Presburger tree automata (PTA) and show how it can be used to express numerical document queries. Surprisingly, the complexity of satisfiability for the extended logic is asymptotically the same as for the original logic. The nonemptiness for PTAs is in general pspacecomplete which is moderate given that it is already pspacehard to test whether the complement of a regular expression is nonempty. We also identify a subclass of PTAs with a tractable nonemptiness problem. Further, to decide whether a tree t satisfies a formula # is polynomial in the size of # and linear in the size of t.
Complexity of decision problems for simple regular expressions
 IN PROCEEDINGS OF THE 29TH INTERNATIONAL SYMPOSIUM ON MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE (MFCS 2004
, 2004
"... We study the complexity of the inclusion, equivalence, and intersection problem for simple regular expressions arising in practical XML schemas. These basically consist of the concatenation of factors where each factor is a disjunction of strings possibly extended with ‘∗ ’ or ‘?’. We obtain lower ..."
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Cited by 27 (12 self)
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We study the complexity of the inclusion, equivalence, and intersection problem for simple regular expressions arising in practical XML schemas. These basically consist of the concatenation of factors where each factor is a disjunction of strings possibly extended with ‘∗ ’ or ‘?’. We obtain lower and upper bounds for various fragments of simple regular expressions. Although we show that inclusion and intersection are already intractable for very weak expressions, we also identify some tractable cases. For equivalence, we only prove an initial tractability result leaving the complexity of more general cases open. The main motivation for this research comes from database theory, or more specifically XML and semistructured data. We namely show that all lower and upper bounds for inclusion and equivalence, carry over to the corresponding decision problems for extended contextfree grammars and singletype tree grammars, which are abstractions of DTDs and XML Schemas, respectively. For intersection, we show that the complexity only carries over for DTDs.
Towards practical typechecking for macro tree transducers
, 2007
"... Abstract. Macro tree transducers (mtt) are an important model that both covers many useful XML transformations and allows decidable exact typechecking. This paper reports our first step toward an implementation of mtt typechecker that has a practical efficiency. Our approach is to represent an input ..."
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Cited by 12 (1 self)
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Abstract. Macro tree transducers (mtt) are an important model that both covers many useful XML transformations and allows decidable exact typechecking. This paper reports our first step toward an implementation of mtt typechecker that has a practical efficiency. Our approach is to represent an input type obtained from a backward inference as an alternating tree automaton, in a style similar to Tozawa’s XSLT0 typechecking. In this approach, typechecking reduces to checking emptiness of an alternating tree automaton. We propose several optimizations (Cartesian factorization, state partitioning) on the backward inference process in order to produce much smaller alternating tree automata than the naive algorithm, and we present our efficient algorithm for checking emptiness of alternating tree automata, where we exploit the explicit representation of alternation for local optimizations. Our preliminary experiments confirm that our algorithm has a practical performance that can typecheck simple transformations with respect to the full XHTML in a reasonable time. 1
Automata, Logic, and XML
 In CSL‘02  Annual Conference of the European Association for Computer Science Logic (invited talk
, 2002
"... We survey some recent developments in the broad area of automata and logic which are motivated by the advent of XML. In particular, we consider unranked tree automata, treewalking automata, and automata over infinite alphabets. We focus on their connection with logic and on questions imposed by ..."
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Cited by 6 (0 self)
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We survey some recent developments in the broad area of automata and logic which are motivated by the advent of XML. In particular, we consider unranked tree automata, treewalking automata, and automata over infinite alphabets. We focus on their connection with logic and on questions imposed by XML.
XML Type Checking Using HighLevel Tree Transducer
 In Functional and Logic Programming (FLOPS
, 2006
"... XML type checking recently attracts interests of researchers. We discuss this problem for programs using higher order functions. In particular, we discuss programs modeled by the highlevel tree transducer which was introduced by Engelfriet. We give one algorithm of XML type checking for this tra ..."
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Cited by 6 (1 self)
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XML type checking recently attracts interests of researchers. We discuss this problem for programs using higher order functions. In particular, we discuss programs modeled by the highlevel tree transducer which was introduced by Engelfriet. We give one algorithm of XML type checking for this transducer.
Welldefinedness and semantic typechecking in the nested relational calculus and xquery
 Theoretical Computer Science
, 2005
"... Abstract. Two natural decision problems regarding the XML query language XQuery are welldefinedness and semantic typechecking. We study these problems in the setting of a relational fragment of XQuery. We show that welldefinedness and semantic typechecking are undecidable, even in the positivee ..."
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Cited by 6 (3 self)
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Abstract. Two natural decision problems regarding the XML query language XQuery are welldefinedness and semantic typechecking. We study these problems in the setting of a relational fragment of XQuery. We show that welldefinedness and semantic typechecking are undecidable, even in the positiveexistential case. Nevertheless, for a “pure” variant of XQuery, in which no identification is made between an item and the singleton containing that item, the problems become decidable. We also consider the analogous problems in the setting of the nested relational calculus. 1
Models of Tree Translation
"... This first chapter gives an introduction into the area of tree transducer theory, and describes the results presented in Chapters 2–6. The first section addresses general issues like translations, trees, and tree grammars. Section 2 is concerned with the different models of tree transducers that ar ..."
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Cited by 4 (1 self)
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This first chapter gives an introduction into the area of tree transducer theory, and describes the results presented in Chapters 2–6. The first section addresses general issues like translations, trees, and tree grammars. Section 2 is concerned with the different models of tree transducers that are considered in the thesis. It describes the typical problems that appear in tree transducer theory, and mentions important properties of the different tree transducer models. Section 3 describes the results of