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Data Exchange: Semantics and Query Answering
 In ICDT
, 2003
"... Data exchange is the problem of taking data structured under a source schema and creating an instance of a target schema that reflects the source data as accurately as possible. In this paper, we address foundational and algorithmic issues related to the semantics of data exchange and to query answe ..."
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Cited by 323 (34 self)
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Data exchange is the problem of taking data structured under a source schema and creating an instance of a target schema that reflects the source data as accurately as possible. In this paper, we address foundational and algorithmic issues related to the semantics of data exchange and to query answering in the context of data exchange. These issues arise because, given a source instance, there may be many target instances that satisfy the constraints of the data exchange problem. We give an algebraic specification that selects, among all solutions to the data exchange problem, a special class of solutions that we call universal. A universal solution has no more and no less data than required for data exchange and it represents the entire space of possible solutions. We then identify fairly general, and practical, conditions that guarantee the existence of a universal solution and yield algorithms to compute a canonical universal solution efficiently. We adopt the notion of "certain answers" in indefinite databases for the semantics for query answering in data exchange. We investigate the computational complexity of computing the certain answers in this context and also study the problem of computing the certain answers of target queries by simply evaluating them on a canonical universal solution.
TwoDimensional Languages
, 1997
"... this paper, much work have been done in studying properties of picture languages recognized by finitestate machines and several other models have been designed. A survey on this subject can be found in [21]. An intersting model of twodimensional tape acceptor is the twodimensional online tessell ..."
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Cited by 57 (3 self)
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this paper, much work have been done in studying properties of picture languages recognized by finitestate machines and several other models have been designed. A survey on this subject can be found in [21]. An intersting model of twodimensional tape acceptor is the twodimensional online tessellation automaton introduced by K. Inoue and A. Nakamura in [18]. This is defined as an infinite twodimensional array of identical conventional finitestate automata and it is a special type of cellular automaton. Despite it is not evident that it is a generalization of a onedimensional model, it can be easily 2 identified to a conventional automaton when restricted to onerow (or onecolumn) pictures. Moreover, the family of picture languages recognized by this model of automaton satisfy many important properties. Different systems to generate pictures using grammars have been also explored (cf. [31, 32, 33, 35, 34, 36, 29, 30, 39]). However, in the finite state case, this approach is shown to be less powerful than others. Another possible generalization is to describe picture languages by logic formulas. Recently, W. Thomas gave a general formalism to describe graphs (and, in particular, pictures) as model theoretical structures and showed as "recognizability" corresponds to the notions of definability on existential monadic second order logic (cf. [38]). This is coherent with the string language recognizability theory where Buchi's Theorem holds. In a recent proposal (cf. [13, 14]) a notion of recognizability of a set of pictures in terms of tiling systems is introduced. The underlying idea is to define recognizability by "projection of local properties". Informally, recognition in a tiling system is defined in terms of a finite set of square pictures of side two which c...
L.: Locally consistent transformations and query answering in data exchange
 In: Proceedings PODS’04
, 2004
"... Data exchange is the problem of taking data structured under a source schema and creating an instance of a target schema. Given a source instance, there may be many solutions – target instances that satisfy the constraints of the data exchange problem. Previous work has identified two classes of des ..."
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Cited by 48 (17 self)
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Data exchange is the problem of taking data structured under a source schema and creating an instance of a target schema. Given a source instance, there may be many solutions – target instances that satisfy the constraints of the data exchange problem. Previous work has identified two classes of desirable solutions: canonical universal solutions, and their cores. Query answering in data exchange amounts to rewriting a query over the target schema to another query that, over a materialized target instance, gives the result that is semantically consistent with the source. A basic question is then whether there exists a transformation sending a source instance into a solution over which target queries can be answered. We show that the answer is negative for many data exchange transformations that have structural properties similar to canonical universal solutions and cores. Namely, we prove that many such transformations preserve the local structure of the data. Using this notion, we further show that every target query rewritable over such a transformation cannot distinguish tuples whose neighborhoods in the source are similar. This gives us a first tool that helps check whether a query is rewritable. We also show that these results are robust: they hold for an extension of relational calculus with grouping and aggregates, and for two different semantics of query answering. 1.
New Techniques for Studying Set Languages, Bag Languages and Aggregate Functions
, 1994
"... We provide new techniques for the analysis of the expressive power of query languages for nested collections. These languages may use set or bag semantics and may be further complicated by the presence of aggregate functions. We exhibit certain classes of graphs and prove that the properties of thes ..."
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Cited by 42 (25 self)
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We provide new techniques for the analysis of the expressive power of query languages for nested collections. These languages may use set or bag semantics and may be further complicated by the presence of aggregate functions. We exhibit certain classes of graphs and prove that the properties of these graphs that can be tested in such languages are either finite or cofinite. This result settles the conjectures of Grumbach, Milo, and Paredaens that parity test, transitive closure, and balanced binary tree test are not expressible in bag languages like the PTIME fragment of BALG of Grumbach and Milo and BQL of Libkin and Wong. Moreover, it implies that many recursive queries, including simple ones like the test for a chain, cannot be expressed in a nested relational language even when aggregate functions are available. In an attempt to generalize the finitecofiniteness result, we study the bounded degree property which says that the number of distinct in and outdegrees in the output of...
Local Properties of Query Languages
"... predeterminedportionoftheinput.Examplesincludeallrelationalcalculusqueries. everyrelationalcalculus(rstorder)queryislocal,thegeneralresultsprovedforlocalqueriescan manyeasyinexpressibilityproofsforlocalqueries.Wethenconsideracloselyrelatedproperty, namely,theboundeddegreeproperty.Itdescribestheoutp ..."
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Cited by 33 (21 self)
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predeterminedportionoftheinput.Examplesincludeallrelationalcalculusqueries. everyrelationalcalculus(rstorder)queryislocal,thegeneralresultsprovedforlocalqueriescan manyeasyinexpressibilityproofsforlocalqueries.Wethenconsideracloselyrelatedproperty, namely,theboundeddegreeproperty.Itdescribestheoutputsoflocalqueriesonstructuresthat locallylook\simple."Everyquerythatislocalisshowntohavetheboundeddegreeproperty.Since Westartbyprovingageneralresultdescribingoutputsoflocalqueries.Thisresultleadsto toapplythanEhrenfeuchtFrassegames.Wealsoshowthatsomegeneralizationsofthebounded degreepropertythatwereconjecturedtohold,failforrelationalcalculus. beviewedas\otheshelf"strategiesforprovinginexpressibilityresults,whichareofteneasier maintenanceofviews,andshowthatSQLandrelationalcalculusareincapableofmaintainingthe gregates,whichisessentiallyplainSQL,hastheboundeddegreeproperty,thusansweringaques tionthathasbeenopenforseveralyears.Consequently,rstorderquerieswithHartigorRescher quantiersalsohavetheboundeddegreeproperty.Finally,weapplyourresultstoincremental Wethenprovethatthelanguageobtainedfromrelationalcalculusbyaddinggroupingandag
Linear Time Computable Problems and FirstOrder Descriptions
, 1996
"... this article is a proof that each FO problem can be solved in linear time if only relational structures of bounded degree are considered. The basic idea of the proof is a localization technique based on a method that was originally developed by Hanf (Hanf 1965) to show that the elementary theories o ..."
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Cited by 31 (2 self)
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this article is a proof that each FO problem can be solved in linear time if only relational structures of bounded degree are considered. The basic idea of the proof is a localization technique based on a method that was originally developed by Hanf (Hanf 1965) to show that the elementary theories of two structures are equal under certain conditions, i.e., that two structures agree on all firstorder sentences. Fagin, Stockmeyer and Vardi (Fagin et al. 1993) developed a variant of this technique, which is applicable in descriptive complexity theory to classes of finite relational structures of uniformly bounded degree. Variants of this result can also be found in Gaifman (1982) (see also Thomas (1991)). The essential content of this result, which is also called the HanfSphere Lemma, is that two relational structures of bounded degree satisfy the same firstorder sentences of a certain quantifierrank if both contain, up to a certain number m, the same number of isomorphism types of substructures of a bounded radius r. In addition, a technique of model interpretability from Rabin (1965) (see also Arnborg et al. (1991), Seese (1992), Compton and Henson (1987) and Baudisch et al. (1982)) is adapted to descriptive complexity classes, and proved to be useful for reducing the case of an arbitrary class of relational structures to a class of structures consisting only of the domain and one binary irreflexive and symmetric relation, i.e., the class of simple graphs. It is shown that the class of simple graphs is lintimeuniversal with respect to firstorder logic, which shows that many problems on descriptive complexity classes, described in languages extending firstorder logic for arbitrary structures, can be reduced to problems on simple graphs. This paper is organized as f...
On Winning Strategies With Unary Quantifiers
 J. Logic and Computation
, 1996
"... A combinatorial argument for two finite structures to agree on all sentences with bounded quantifier rank in firstorder logic with any set of unary generalized quantifiers, is given. It is known that connectivity of finite structures is neither in monadic \Sigma 1 1 nor in L !! (Q u ), where Q ..."
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Cited by 25 (6 self)
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A combinatorial argument for two finite structures to agree on all sentences with bounded quantifier rank in firstorder logic with any set of unary generalized quantifiers, is given. It is known that connectivity of finite structures is neither in monadic \Sigma 1 1 nor in L !! (Q u ), where Q u is the set of all unary generalized quantifiers. Using this combinatorial argument and a combination of secondorder EhrenfeuchtFra iss'e games developed by Ajtai and Fagin, we prove that connectivity of finite structures is not in monadic \Sigma 1 1 with any set of unary quantifiers, even if sentences are allowed to contain builtin relations of moderate degree. The combinatorial argument is also used to show that no class (if it is not in some sense trivial) of finite graphs defined by forbidden minors, is in L !! (Q u ). Especially, the class of planar graphs is not in L !! (Q u ). 1. Introduction The expressive power of firstorder logic L !! is rather limited. This is beca...
Notions of Locality and Their Logical Characterizations Over Finite Models
, 1997
"... Many known tools for proving expressibility bounds for firstorder logic are based on one of several locality properties. In this paper we characterize the relationship between those notions of locality. We note that Gaifman's locality theorem gives rise to two notions: one deals with sentences a ..."
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Cited by 25 (17 self)
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Many known tools for proving expressibility bounds for firstorder logic are based on one of several locality properties. In this paper we characterize the relationship between those notions of locality. We note that Gaifman's locality theorem gives rise to two notions: one deals with sentences and one with open formulae. We prove that the former implies Hanf's notion of locality, which in turn implies Gaifman's locality for open formulae. Each of these implies the bounded degree property, which is one of the easiest tools for proving expressibility bounds. These results apply beyond the firstorder case. We use them to derive expressibility bounds for firstorder logic with unary quantifiers and counting. We also characterize the notions of locality on structures of small degree. 1 Introduction It is well known that firstorder logic has limited expressive power. Typically, inexpressibility proofs are based on either a compactness argument, or EhrenfeuchtFraiss'e games. In ...
Logics with Aggregate Operators
 Journal of the ACM
"... We study adding aggregate operators, such as summing up elements of a column of a relation, to logics with counting mechanisms. The primary motivation comes from database applications, where aggregate operators are present in all real life query languages. Unlike other features of query languages, a ..."
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Cited by 24 (12 self)
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We study adding aggregate operators, such as summing up elements of a column of a relation, to logics with counting mechanisms. The primary motivation comes from database applications, where aggregate operators are present in all real life query languages. Unlike other features of query languages, aggregates are not adequately captured by the existing logical formalisms. Consequently, all previous approaches to analyzing the expressive power of aggregation were only capable of producing partial results, depending on the allowed class of aggregate and arithmetic operations. We consider a powerful counting logic, and extend it with the set of all aggregate operators. We show that the resulting logic satis es analogs of Hanf's and Gaifman's theorems, meaning that it can only express local properties. We consider a database query language that expresses all the standard aggregates found in commercial query languages, and show how it can be translated into the aggregate logic, thereby pro...
Logics For ContextFree Languages
, 1995
"... We define matchings, and show that they capture the essence of contextfreeness. More precisely, we show that the class of contextfree languages coincides with the class of those sets of strings which can be defined by sentences of the form 9 b', where ' is first order, b is a binary predicate sym ..."
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Cited by 23 (5 self)
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We define matchings, and show that they capture the essence of contextfreeness. More precisely, we show that the class of contextfree languages coincides with the class of those sets of strings which can be defined by sentences of the form 9 b', where ' is first order, b is a binary predicate symbol, and the range of the second order quantifier is restricted to the class of matchings. Several variations and extensions are discussed.