On the expressive power of the relational algebra

Paredaens, Jan

doi:10.1016/0020-0190(78)90055-8

Cited by 77 publications

(52 citation statements)

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“…(A similar duality exists in the relational database model, where Bancilhon [1] and Paredaens [21] considered and characterized expressiveness at the instance level, which, subsequently, Chandra and Harel [7] contrasted with expressiveness at the query level. )…”

Section: Introductionmentioning

confidence: 82%

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

Gyssens

Paredaens

Gucht

et al. 2006

Proceedings of the Twenty-Fifth ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems

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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. We give characterizations, in terms of the structure of D, for when a binary relation on its nodes is definable by an XPath expression in these fragments. Since each pair of nodes in such a relation represents a unique path in D, our results therefore capture the sets of paths in D definable in XPath. We refer to this perspective on the semantics of XPath as the "global view." In contrast with this global view, there is also a "local view" where one is interested in the nodes to which one can navigate starting from a particular node in the document. 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. All these definability results, both in the global and the local view, are obtained by using a robust two-step methodology, which consists of first characterizing when two nodes cannot be distinguished by an expression in the respective fragments of XPath, and then bootstrapping these characterizations to the desired results.

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Section: Introductionmentioning

confidence: 82%

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

Gyssens

Paredaens

Gucht

et al. 2006

Proceedings of the Twenty-Fifth ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems

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“…Codd's pioneering work [Codd] on the relational calcuhts and algebra, a lot of work has been done on studying and comparing the expressive power of several query languages [AU,Ba,Cttl,CII2.CH3,Chan,Coop,Pa].…”

Section: Introductionmentioning

confidence: 99%

The complexity of relational query languages (Extended Abstract)

Vardi¹

1982

Proceedings of the Fourteenth Annual ACM Symposium on Theory of Computing - STOC '82

1,019

660

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Two complexity measures for query languages are proposed. Data complexity is the complexity of evaluating a query in the language as a function of the size of the database, and expression complexity is the complexity of ewduating a query in the language as a function of the size of the expression defining the query. We study the data and expression complexity of logical langnages -relational calculus and its extensions by transitive closure, fixpoint and second order existential quantification -and algebraic languages -relational algebra and its extensions by bounded and unbounded looping. The pattern which will bc shown is that the expression complexity of the investigated languages is one exponential higher then their data complexity, and for both types of complexity we show completeness in some complexity class.

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“…The syntax of the fragment XQ is shown in Figure 1, by rules [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] 3 . This syntax is an abstract syntax 4 .…”

Section: Syntaxmentioning

confidence: 99%

“…It was not until recently that similar efforts were made for XQuery: Koch studies the computational complexity of nonrecursive XQuery [9], Vansummeren looks into the well-definedness problem for XQuery fragments [13] and the expressive power of the node construction in XQuery is studied in [10]. In this paper we will investigate the expressive power of XQuery fragments in a similar fashion as was done for the relational algebra [12] and SQL [11]. In order to do this, we establish some interesting properties for these fragments.…”

Section: Introductionmentioning

confidence: 99%

On the Expressive Power of XQuery Fragments

Hidders

Marrara

Paredaens

et al. 2005

Database Programming Languages

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Abstract. XQuery is known to be a powerful XML query language with many bells and whistles. For many common queries we do not need all the expressive power of XQuery. We investigate the effect of omitting certain features of XQuery on the expressive power of the language. We start from a simple base fragment which can be extended by several optional features being aggregation functions such as count and sum, sequence generation, node construction, position information in for loops, and recursion. In this way we obtain 64 different XQuery fragments which can be divided into 17 different equivalence classes such that two fragments can express the same functions iff they are in the same equivalence class. Moreover, we investigate the relationships between these equivalence classes.

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On the expressive power of the relational algebra

Cited by 77 publications

References 1 publication

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

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

The complexity of relational query languages (Extended Abstract)

On the Expressive Power of XQuery Fragments

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