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22
TWOWAY UNARY TEMPORAL LOGIC OVER TREES
, 2009
"... We consider a temporal logic EF + F −1 for unranked, unordered finite trees. The logic has two operators: EFϕ, which says “in some proper descendant ϕ holds”, and F −1 ϕ, which says “in some proper ancestor ϕ holds”. We present an algorithm for deciding if a regular language of unranked finite tree ..."
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We consider a temporal logic EF + F −1 for unranked, unordered finite trees. The logic has two operators: EFϕ, which says “in some proper descendant ϕ holds”, and F −1 ϕ, which says “in some proper ancestor ϕ holds”. We present an algorithm for deciding if a regular language of unranked finite trees can be expressed in EF+F −1. The algorithm uses a characterization expressed in terms of forest algebras.
A decidable characterization of locally testable tree languages
 In ICALP (2
"... Vol. 7 (4:03) 2011, pp. 1–25 www.lmcsonline.org ..."
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Characterization of Logics Over Ranked Tree Languages
"... Abstract. We study the expressive power of the logics EF + F −1, ∆2 and boolean combinations of Σ1 over ranked trees. In particular, we provide effective characterizations of those three logics using algebraic identities. Characterizations had already been obtained for those logics over unranked tre ..."
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Abstract. We study the expressive power of the logics EF + F −1, ∆2 and boolean combinations of Σ1 over ranked trees. In particular, we provide effective characterizations of those three logics using algebraic identities. Characterizations had already been obtained for those logics over unranked trees, but both the algebra and the proofs were dependant on the properties of the unranked structure and the problem remained open for ranked trees. 1
Effective characterizations of tree logics
, 2008
"... A survey of effective characterizations of tree logics. If L is a logic, then an effective characterization for L is an algorithm, which inputs a tree automaton and replies if the recognized language can be defined by a formula in L. The logics L considered include path testable languages, frontier ..."
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Cited by 5 (1 self)
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A survey of effective characterizations of tree logics. If L is a logic, then an effective characterization for L is an algorithm, which inputs a tree automaton and replies if the recognized language can be defined by a formula in L. The logics L considered include path testable languages, frontier testable languages, fragments of Core XPath, and fragments of monadic secondorder logic.
View update translation for XML
 in "14th International Conference on Database Theory (ICDT
"... We study the problem of update translation for views on XML documents. More precisely, given an XML view definition and a user defined view update program, find a source update program that translates the view update without side effects on the view. Additionally, we require the translation to be de ..."
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We study the problem of update translation for views on XML documents. More precisely, given an XML view definition and a user defined view update program, find a source update program that translates the view update without side effects on the view. Additionally, we require the translation to be defined on all possible source documents; this corresponds to Hegner’s notion of uniform translation. The existence of such translation would allow to update XML views without the need of materialization. The class of views we consider can remove parts of the document and rename nodes. Our update programs define the simultaneous application of a collection of atomic update operations among insertion/deletion of a subtree and node renaming. Such update programs are compatible with the XQuery Update Facility (XQUF) snapshot semantics. Both views and update programs are represented by recognizable tree languages. We present as a proof of concept a small fragment of XQUF that can be expressed by our update programs, thus allows for update propagation. Two settings for the update problem are studied: without source constraints, where all source updates are allowed, and with source constraints, where there is a restricted set of authorized source updates. Using tree automata techniques, we establish that without constraints, all view updates are uniformly translatable and the translation is tractable. In presence of constraints, not all view updates are uniformly translatable. However, we introduce a reasonable restriction on update programs for which uniform translation with constraints becomes possible. All authors are members of MOSTRARE, joint team of
Algebra for trees
 In Handbook of Automata Theory. European Mathematical Society Publishing
"... Abstract. This chapter presents several algebraic approaches to tree languages. The idea is to design a notion for trees that resembles semigroups or monoids for words. The focus is on the connection between the structure of an algebra recognizing a tree language, and the kind of logic needed to def ..."
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Abstract. This chapter presents several algebraic approaches to tree languages. The idea is to design a notion for trees that resembles semigroups or monoids for words. The focus is on the connection between the structure of an algebra recognizing a tree language, and the kind of logic needed to define the tree language. Four algebraic approaches are described in this chapter: trees as terms of universal algebra, preclones, forest algebra, and seminearrings. Each approach is illustrated with an application to logic on trees. 1
Decidable classes of documents for XPath
"... We study the satisfiability problem for XPath over XML documents of bounded depth. We define two parameters, called match width and braid width, that assign a number to any class of documents. We show that for all k, satisfiability for XPath restricted to bounded depth documents with match width at ..."
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We study the satisfiability problem for XPath over XML documents of bounded depth. We define two parameters, called match width and braid width, that assign a number to any class of documents. We show that for all k, satisfiability for XPath restricted to bounded depth documents with match width at most k is decidable; and that XPath is undecidable on any class of documents with unbounded braid width. We conjecture that these two parameters are equivalent, in the sense that a class of documents has bounded match width iff it has bounded braid width.
Regular languages of thin trees
"... An infinite tree is called thin if it contains only countably many infinite branches. Thin trees can be seen as intermediate structures between infinite words and infinite trees. In this work we investigate properties of regular languages of thin trees. Our main tool is an algebra suitable for thin ..."
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An infinite tree is called thin if it contains only countably many infinite branches. Thin trees can be seen as intermediate structures between infinite words and infinite trees. In this work we investigate properties of regular languages of thin trees. Our main tool is an algebra suitable for thin trees. Using this framework we characterize various classes of regular languages: commutative, open in the standard topology, closed under two variants of bisimulational equivalence, and definable in WMSO logic among all trees. We also show that in various meanings thin trees are not as rich as all infinite trees. In particular we observe a parity index collapse to level (1, 3) and a topological complexity collapse to coanalytic sets. Moreover, a gap property is shown: a regular language of thin trees is either WMSOdefinable among all trees or coanalyticcomplete.