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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
Manipulating Spatial Data in Constraint Databases
, 1997
"... . Constraint databases have recently been proposed as a powerful framework to model and retrieve spatial data. In a constraint database, a spatial object is represented as a quantifier free conjunction of (usually linear) constraints, called generalized tuple. The set of solutions of such quantifier ..."
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Cited by 25 (4 self)
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. Constraint databases have recently been proposed as a powerful framework to model and retrieve spatial data. In a constraint database, a spatial object is represented as a quantifier free conjunction of (usually linear) constraints, called generalized tuple. The set of solutions of such quantifier free formula represents the set of points belonging to the extension of the object. The relational algebra can be easily extended to deal with generalized relations. However, such algebra has some limitations when it is used for modeling spatial data. First of all, there is no explicit way to deal with the set of points representing a spatial object as a whole. Rather, only pointbased computations can be performed using this algebra. Second, practical constraint database languages typically use linear constraints. This allows to use efficient algorithms but, at the same time, some interesting queries cannot be represented (for example, the distance between two objects cannot be computed). ...
An Extended Algebra for Constraint Databases
 IEEE Transactions on Knowledge and Data Engineering
, 1999
"... Constraint relational databases use constraints to both model and query data. A constraint relation contains a finite set of generalized tuples. Each generalized tuple is represented by a conjunction of constraints on a given logical theory and, depending on the logical theory and the specific conju ..."
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Cited by 20 (3 self)
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Constraint relational databases use constraints to both model and query data. A constraint relation contains a finite set of generalized tuples. Each generalized tuple is represented by a conjunction of constraints on a given logical theory and, depending on the logical theory and the specific conjunction of constraints, it may possibly represent an infinite set of relational tuples. For their characteristics, constraint databases are well suited to model multidimensional and structured data, like spatial and temporal data. The definition of an algebra for constraint relational databases is important in order to make constraint databases a practical technology. In this paper, we extend the previously defined constraint algebra (called generalized relational algebra). First, we show that the relational model is not the only possible semantic reference model for constraint relational databases and we show how constraint relations can be interpreted under the nested relational model. Then...
Incremental Recomputation of Recursive Queries with Nested Sets and Aggregate Functions
, 1997
"... We examine the power of incremental evaluation systems that use an SQLlike language for maintaining recursivelydefined views. We show that recursive queries such as transitive closure, and "alternating paths" can be incrementally maintained in a nested relational language, when some auxiliary r ..."
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Cited by 18 (7 self)
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We examine the power of incremental evaluation systems that use an SQLlike language for maintaining recursivelydefined views. We show that recursive queries such as transitive closure, and "alternating paths" can be incrementally maintained in a nested relational language, when some auxiliary relations are allowed. In the presence of aggregate functions, even more queries can be maintained, for example, the "same generation" query. In contrast, it is still an open problem whether such queries are maintainable in relational calculus. We then restrict the language so that no nested relations are involved (but wekeep the aggregate functions). Such a language captures the capability of most practical relational database systems. We prove that this restriction does not reduce the incremental computational power; that is, any query that can be maintained in a nested language with aggregates, is still maintainable using only flat relations. We also show that one does not need auxiliar...
SQL Can Maintain PolynomialHierarchy Queries
, 1997
"... this report, we only consider queries from flat relations to flat relations; and the criteria for permissible update is restricted to the insertion and deletion of a single tuple. A restriction is also imposed so that the constants that appear in the auxiliary database must also appear in the databa ..."
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Cited by 2 (2 self)
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this report, we only consider queries from flat relations to flat relations; and the criteria for permissible update is restricted to the insertion and deletion of a single tuple. A restriction is also imposed so that the constants that appear in the auxiliary database must also appear in the database or in the answer or in some fixed set. In this report, this fixed set is Q , the set of rational numbers. We use the firstorder incremental evaluation system, IES(FO)(called FOIES in [10]), to illustrate the concept. IES(FO) uses firstorder logic to express update functions [9, 11]. For each relation symbol R,
Finitely Representable Nested Relations
"... this paper is the definition of a model and a query language for finitely representable nested relations, overcoming some limitations of the previous proposals. Our language is obtained by extending ..."
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Cited by 1 (1 self)
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this paper is the definition of a model and a query language for finitely representable nested relations, overcoming some limitations of the previous proposals. Our language is obtained by extending
Updating Complex Value Databases
, 1998
"... Query languages and their optimizations have been a very important issue in the database community. Languages for updating databases, however, have not been studied to the same extent, although they are clearly important since databases must change over time. The structure and expressiveness of upda ..."
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Cited by 1 (1 self)
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Query languages and their optimizations have been a very important issue in the database community. Languages for updating databases, however, have not been studied to the same extent, although they are clearly important since databases must change over time. The structure and expressiveness of updates is largely dependent on the data model. In relational databases, for example, the update language typically allows the user to specify changes to individual fields of a subset of a relation that meets some selection criterion. The syntax is terse, specifying only the pieces of the database that are to be altered. Because of its simplicity, most of the optimizations take place in the internal processing of the update rather than at the language level. In complex value databases, the need for a terse and optimizable update language is much greater, due to the deeply nested structures involved. Starting with a query language for complex value databases called the Collection Programming Lang...