S. Abiteboul and C. Beeri. The power of languages for the manipulation of complex values. VLDB Journal, 4(4):727--794, 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....allowing the handling of in nite relations (for instance, representing spatial and temporal data) although nitely representable, and the querying mechanism deals eciently with this nite representation. On the other hand, as in the relational database model, di erent calculi and algebras [1, 12, 19, 7] have been developed as query formalisms for these new database paradigms. These calculi and algebras extend the relational calculus and algebra, by adding the handling of complex values and constraints. In the case of complex values [1] the calculi extend the relational rst order logic, for ....

....database model, di erent calculi and algebras [1, 12, 19, 7] have been developed as query formalisms for these new database paradigms. These calculi and algebras extend the relational calculus and algebra, by adding the handling of complex values and constraints. In the case of complex values [1], the calculi extend the relational rst order logic, for instance, with equality, membership and inclusion relations over sets. In the case of constraint This work has been partially supported by the Spanish project INDALOG TIC200203968 databases, the calculi extend relational rst order ....

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S. Abiteboul and C. Beeri. The Power of Languages for the Manipulation of Complex Values. VLDB, 4(4):727-794, 1995.

....to consider an extended relational calculus as query language, which handles the proposed data model; and nally, 3) to provide semantic foundations to the new query language. With respect to (1) the underlying data model of functional logic programming is complex from a database point of view [1]. Firstly, types can be de ned by using recursively de ned datatypes, as lists and trees. Therefore, the attribute values can be multi valued ; that is, more than one value (for instance, a set of values enclosed in a list) for a given attribute corresponds to each set of key attributes. In ....

....and (b) the output relation only depends on the input relations. In general, it is undecidable, and therefore syntactic conditions have to be developed in such a way that, only the so called safe queries (satisfying these conditions) ensure the property of domain independence. For instance, [1] and [10] propose syntactic conditions, which allow the building of safe formulas in a relational calculus with complex values and linear constraints, respectively. In this line, we have developed syntactic conditions over our query language, which allow the building of the so called safe ....

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S. Abiteboul and C. Beeri. The Power of Languages for the Manipulation of Complex Values. VLDB, 4(4):727-794, 1995.

....require effective storage, efficient access and inference of large amounts of data with complex structures. However, such capabilities are not directly supported by the existing database systems. In the past decade, various advanced data models such as nested relational and complex object models [1, 3, 9, 14, 19, 28, 31, 32] and object oriented models [5, 11, 15, 17, 18] were developed to support the storage of large amounts of data with complex structures. On the other hand, a lot of interests arose in the deductive database approach which integrates the logic programming and relational database techniques and ....

S. Abiteboul and C. Beeri. The Power of Languages for the Manipulation of Complex Values. VLDB Journal, 4(4):727-- 794, 1995.

....(n) grows very slowly) 8. Logic programming with equality The relational model of data deals with simple values, namely tuples consisting of atomic components. Various generalizations and formalisms have been proposed to handle more complex values like nested tuples, tuples of sets, etc. [1]. Most of these formalisms can be expressed in terms of LP with equality [62, 63, 74, 72, 39] and constraint logic programming considered in Section 9. 8.1. Equational theories Let L be a language containing the equality predicate = By an equation over L we mean an atom s = t where s and t are ....

....set of trees. In the case of logic programming with sets, an input may be a set whose elements may be sets too and so on. Various models and languages for dealing with complex values in databases have been proposed. The comparative expressive power of such formalisms is studied, for example, in [1]. This paper introduces a model for restricted combinations of tuples and sets and several corresponding query languages, including the algebraic and logic programming ones. It is proved that all these languages define the same class of queries. The absolute expressive power of such languages (in ....

S. Abiteboul and C. Beeri. The power of languages for the manipulation of complex values. VLDB J., 4:727--794, 1995.

....the result of applying to atomic values two constructors: a tuple constructor to make tuples and a set constructor to make sets of tuples. Complex objects allow the application of the tuple and set constructor recursively. For nested relations, set and tuple constructors are required to alternate [1]. De nition A relation scheme R is recursively de ned by the following rules: 1) if fA 1 ; A k g att and A 1 ; A k are atomic valued attributes, then R = A 1 ; A k ) is a relation scheme. 2) if fA 1 ; A k g att and A 1 ; A k are atomic valued attributes, R 1 ; ....

....The resulting equivalent expression is more ecient than the original one. 7 Conclusion The nested relational model provides a better way of representing complex objects than the traditional relational model, and allows users to describe their concepts of real world data objects more easily [1, 3, 21] However, the optimization of queries is di erent from that in the 1NF relational model. In this paper we have investigated some algebraic properties of nested relational operators which are useful for query optimization in the nested relational model. We have discussed the interactions of ....

S. Abiteboul and C. Beeri. On the power of languages for the manipulation of complex values. In The Journal of Very Large Data Bases, 4(4), 1995.

....adom(q) 2] 3 Safety and Evaluation It is a general approach that enforces syntactic restrictions on queries so that they become domain independent. The definition of the class of safe queries is a generalisation of the class of safe queries presented previously for the complex object model [1, 2] and for an arithmetic relational model [9] 3.1 Safety We extend the definition of safe query for our arithmetic complex value model. A DB satisfies a finiteness dependency on an argument x of predicate p if, for every fixed instance of arguments t i , t i 6= x, such that the predicate is ....

....p if, for every fixed instance of arguments t i , t i 6= x, such that the predicate is true, the set of instances of x is finite. For example, the predicate x y =z has finiteness dependency on z (or on x or y) We add the following rule to the notion of range restricted which is defined in[1]. ffl F is an arithmetic predicate p(t 1 ; t n ) some t j is x, there exists a finite dependency in the predicate p and every variable in p except x is range restricted relative to the ordering. The set of variables which precedes x in the ordering are used to propagate bindings and have ....

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S. Abiteboul and C. Beeri. On the power of languages for the manipulation of complex values. In The Journal of Very Large Data Bases, 4(4):727-794, 1995.

....genericity and domain independence. So we need to reconsider what type of queries is safe , that is a query which can be answered sensibly. Some attempts to extend the definition of domain independence for the complex value data model extended with external functions have already been made [1, 17]. None of these attempts, however, address the aspects of calculus queries with fix points and the relationship between safety, extended domain independence, and finiteness. The first goal of this paper is to investigate the notion of domain independence of complex value calculus queries with ....

....domain independence. The notion of embedded domain independence was proposed to generalize domain independence to incorporate functions [8] The fundamental idea behind this notion is that, for any query q, there is a bound on the number of times functions (and their inverses) can be applied [1]. The answer to q on an input instance I depends on the closure of adom(q, I) We review this notion for complex objects as follows. Given a database instance I and a query q, let C q be a set of constants that appear in q. Following [1] we define term n (DB) for some database DB with ....

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S. Abiteboul and C. Beeri. On the power of languages for the manipulation of complex values. In The Journal of Very Large Data Bases, 4(4):727-794, 1995.

....below: 1) Integration of data The CAD data is accessed by di erent CAD tools. Each tool might have its own view of data. All these di erent aspects of data can be stored in separate databases, but this will lead to inconsistencies in data during updates. Hence an integrated CAD database is sought[5]. If an integrated CAD database hasto be developed then all aspects of an design object has to be stored and it has to be made easily accessible. For example, a schematic or structural view of a Levelling xture, will represent the subparts of the levelling xture, a behavioural view has details ....

....data, we have to join the relations which is a very expensive operation when the volume of data is large. Besides, inconsistencies in data can easily occur when updating the data. The problem in fact lines in the rst normal form constraint. 5 Complex Value Databases Complex value databases [2, 5, 9, 10, 18, 19, 20] relax the rst normal form constraint imposed on the relational databases. The tuple components of a relation can be complex values, such as tuples, sets or even relations themselves. Complex values are formed from atomic values such as integers, reals, strings, characters, etc. using the tuple ....

Serge Abiteboul and Catriel Beeri. The Power of Languages for the Manipulation of Complex Values. VLDB Journal, 4(4):727-794, 1995.

....of data with complex structures. In this paper, we describe query processing in the Relationlog system. In particular, we illustrate the extended semi naive and magic set techniques used in Relationlog. 1 Introduction During the past decades, the nested relational and complex object models [1, 5, 11, 12, 15, 18, 21, 22] were developed to extend the applicability of the traditional relational model to more complex, non business applications such as CAD, image processing and text retrieval [2] Another important direction of intense research has been in using a logic programming based language Datalog [8, 23] as ....

.... several years, there have been some e orts to combine these two approaches, mainly by extending Datalog with set and tuple constructors [3, 7, 6, 9, 13, 14, 19] Like Datalog, their natural use of xpoint construct allows to express transitive closure declaratively in polynomial space and time [4, 5], which makes them expressive enough while still practical for real database applications. However, most of the research on such kind of deductive databases stays at the theoretical level. A few implemented systems such as LDL [10] and CORAL [20] are just memory based. In the past few years, we ....

Serge Abiteboul and Catriel Beeri. The Power of Languages for the Manipulation of Complex Values. VLDB Journal, 4(4):727-794, 1995.

....As the relational database technology is inadequate for many advanced applications, it has been extended significantly during the past decade. These extensions can be classified into three kinds: complex object databases, objectoriented databases and deductive databases. Complex object databases [2, 3, 6, 15, 20, 32, 27, 35, 38, 39] relax the first normal form constraint imposed on the relational databases by allowing complex objects to be formed using the tuple and set constructors. Object oriented databases [7, 11, 12, 16, 17, 21, 24, 26] extends data modeling power of the relational databases by means of object identity, ....

Serge Abiteboul and Catriel Beeri. The power of languages for the manipulation of complex values. VLDB Journal, 4(4):727-- 794, 1995.

....trees depending on the signature, range restrictedness and presence of negation. It is possible to reformulate our complexity results in terms of some relational query languages with complex values, using suitable algebraic formalizations corresponding to nonrecursive logic programs, see, e.g. (Abiteboul Beeri 1995). Results of this paper show that nonrecursive query languages for complex values are highly intractable. It will be interesting to investigate these classes in terms of fixed parameter complexity similar to the analysis done in (Papadimitriou Yannakakis 1997, Vardi 1995) We briefly mention ....

....logic programming with complex values depends on this formalization and the signature, i.e. the set of operations available on the values. We consider 1. colored finite sets (Dovier et al. 1996) 2. untyped finite sets (Dantsin Voronkov 1997a, Dantsin Voronkov 1997b) 3. typed finite sets (Abiteboul Beeri 1995). The definitions and subsequent results can be straightforwardly generalized to finite multisets. 8.1 Formalizations of finite sets Universe with colored sets. In order to construct the domain of colored sets (Dovier et al. 1996) we need to add to a signature Sigma a binary function symbol ....

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Abiteboul, S. & Beeri, C. (1995), `The power of languages for the manipulation of complex values', VLDB Journal 4, 727--794.

....about lists, often used in deductive databases to replace sets and multisets. It is possible to reformulate our complexity results in terms of some relational query languages with complex values, using suitable algebraic formalizations corresponding to nonrecursive logic programs, see, e.g. [1]. Results of this paper show that nonrecursive query languages for complex values are highly intractable. It will be interesting to investigate these classes in terms of fixedparameter complexity similar to the analysis done in [46, 56, 29, 36] We briefly mention some results on the complexity ....

....The complexity of the corresponding nonrecursive fragment of logic programming with complex values depends on this formalization and the signature, i.e. the set of operations available on the values. We consider 1. colored finite sets [22] 2. untyped finite sets [19, 21] 3. typed finite sets [1]. The definitions and subsequent results can be straightforwardly generalized to finite multisets. 6 8.1 Formalizations of finite sets Universe with colored sets. In order to construct the domain of colored sets [22] we need to add to a signature Sigma a binary function symbol f: j : ....

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S. Abiteboul and C. Beeri. The power of languages for the manipulation of complex values. VLDB Journal, 4:727--794, 1995.

....has constant computational cost, uniform construction indeed guarantees tractability of the aggregate functions so defined. We are now ready to address the impact of incorporating aggregate functions in a database query language. To this end, we consider a two sorted algebra for complex values [1], called CVA, over an uninterpreted domain and an interpreted one. In this context, we first study extensions of CVA with built in aggregate functions, that is, with operators whose semantics is defined outside the database. We then present a simple constructor, called folding, that allows the ....

....A( Omega ) depend on properties of the scalar functions in the vocabulary Omega . ut 3 A Query Language with Interpreted Functions In this section we investigate the embedding of a class of aggregate functions within a database query language. We first introduce an algebra for complex values [1], and then extend it with interpreted scalar and aggregate functions. 3.1 The Data Model We consider a two sorted data model for complex values, over a countably infinite, uninterpreted domain D and the interpreted domain Q of the rational numbers. We fix two further countably infinite disjoint ....

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S. Abiteboul and C. Beeri. The power of languages for the manipulation of complex values. The VLDB Journal, 4(4):727--794, October 1995.

....The nested model [14, 18] is an extension of the traditional, flat relational database model in which relations can have both flat, atomic entries and structured, relationvalued entries. Since the late 1980s, various query languages have been considered in the context of the nested model [1, 5, 7, 9, 11, 16, 18]. These languages can be classified according to their expressive power [2] The nested algebra [18] which extends the traditional, flat relational algebra with two restructuring operators, called nest and unnest , can only express a fragment of the polynomial time queries over nested ....

....extends the traditional, flat relational algebra with two restructuring operators, called nest and unnest , can only express a fragment of the polynomial time queries over nested databases. Therefore, several extensions of the nested algebra were proposed, one of which is its fixpoint closure [1, 11], which extends the nested algebra with a fixpoint construct. Although many more polynomial time queries on nested databases can be expressed efficiently in this extended language, it was shown in the aforementioned papers that intractable queries, such as computing the powerset of a relation, can ....

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S. Abiteboul and C. Beeri, "On the Power of Languages for the Manipulation of Complex Values," VLDB Journal, 4(4): 727-794 (1995)

....nested relations, complex values, minimal model semantics, fixpoint semantics. A preliminary version appeared as an extended abstract in the Proceedings of the International Logic Programming Symposium, 1995. 1 Introduction In the past decade, the nested relational and complex value models [2, 14, 17, 21, 25, 26, 6] were developed to extend the applicability of the traditional relational model [13, 28] to more complex, non business applications such as CAD, image processing and text retrieval [3] Extended relational algebra and calculus are provided for such kind of models. It has been proved that extended ....

....algebra and calculus are provided for such kind of models. It has been proved that extended relational algebra without the powerset operator and safe calculus without the subset predicate are equivalent [26] Queries expressed in either framework can be evaluated in polynomial time. It is shown in [6] that extended relational algebra with the powerset operator and safe extended relational calculus with the subset predicate are also equivalent and can simulate iteration and express transitive closure. However, they do so in a very inefficient way. Computations of transitive closure using either ....

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Serge Abiteboul and Catriel Beeri. The power of languages for the manipulation of complex values. VLDB Journal, 4(4):727--794, October 1995.

....6.2 A query q is definable in the relational algebra of trees if and only if q is definable by a range restricted nonrecursive logic program. Proof. The proof is standard and similar to the proof of the equivalence between the relational algebra and range restricted nonrecursive Datalog : e.g. Abiteboul et al. 1995]. 2 Theorem 6.3 A query q is definable by a nonrecursive logic program if and only if q is a boolean combination of queries definable by range restricted nonrecursive logic programs. Therefore, a query q is definable by nonrecursive logic program if and only if q is a boolean combination of ....

....semantics is defined as the class of predicates over the Herbrand base defined in these semantics. There are many results on extensions of Datalog by complex values different from trees, in particular by finite sets and multisets [e.g. Kuper 1990, Abiteboul and Grumbach 1991, Vadaparty 1991, Abiteboul and Beeri 1995, Grumbach and Vianu 1995, Kanellakis, Kuper and Revesz 1995, Dantsin and Voronkov 1997] ....

Abiteboul S. and Beeri C. [1995], `The power of languages for the manipulation of complex values', VLDB Journal 4, 727--794.

....or for an object oriented database, is how expressive it is. For a relational database language such as SQL it is important that it be complete in the sense that it can emulate the relational algebra. For nested relational databases, the standard is the nested relational algebra (NRA) [3], which CPL can easily be shown to emulate [61] However, CPL s type system also contains lists and bags so it can obviously express more than the NRA. The closest comparison to make is therefore with OQL, the query language part of the ODMG proposal [16] to standardize object oriented ....

Serge Abiteboul and Catriel Beeri. The power of languages for the manipulation of complex values. The VLDB Journal, 4:727--794, 1995.

....query processing difficult, but also makes the schema vastly different from the natural representation of the structure. To get around this problem, various forms of complex object models have been proposed. One of the most prominent complexobject models is the nested relational model [TF86, AB95] in which the attributes in a relation are allowed to be of composite type (e.g. sets, lists or other relations) thus making the actual representation of the data in this model closer to its conceptual structure. The schema in Figure 4, using a nested relational model, will have an instance as ....

Serge Abiteboul and Catriel Beeri. The power of languages for the manipulation of complex values. VLDB Journal, 4(4):727--794, October 1995.

....Relational query languages typically deal with tuples of atomic values like strings or integers. Applications require to handle more complex values, for example sets or multisets. Various kinds of complex values in databases and logic programming have been considered in many papers, including [2, 3, 16, 6, 23, 21, 17, 5, 1, 15, 14, 11, 10, 24]. Our paper studies complexity aspects of databases with complex values. There are two main kinds of complexity in databases: 1) query evaluation complexity that measures time or space needed to evaluate a query, and (2) descriptive complexity that characterizes the expressive power of query ....

S. Abiteboul and C. Beeri. The power of languages for the manipulation of complex values. VLDB Journal, 4:727--794, 1995.

....types, our goals also include providing the ability to specificy optimization schemes for constraints. 2 A Constraint based Data Model We introduce a constraint database model that is based on a combination of the constraint database model [6] and the nested relational database model (see e.g. [2]) Specifically, spatial data is treated as (possibly infinite) sets of points in the space with specified dimensions. These sets are then used as values in tuples, similar to the way in which nested relations are used. We first illustrate the constraint database idea with the following example. ....

....on the variable x1 , of the geometry attribute of each tuple in the Cities relation, we write: select cname, region. 1] from Cities To project on several dimensions, e.g. to project a 3dimensional spatial attribute location onto the first two dimensions, we use the notation location. [1,2] in the select where clause. Generalized Functions and Aggregate Functions: In relational SQL, all functions, including aggregate functions, take a single value as input and return a single value. In contrast to this, functions on the spatial component in a database of our model can accept and ....

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S. Abiteboul and C. Beeri. The power of languages for the manipulation of complex values. VLDB Journal, 4(4):727-- 794, October 1995.

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S. Abiteboul and C. Beeri. The power of languages for the manipulation of complex values. VLDB Journal, 4(4):727--794, 1995.

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S. Abiteboul and C. Beeri. The Power of Languages for the Manipulation of Complex Values. VLDB, 4(4):727-794, 1995.

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S. Abiteboul and C. Beeri. The power of languages for the manipulation of complex values. VLDB Journal, 4(4):727--794, October 1995.

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Serge Abiteboul and Catriel Beeri. The power of languages for the manipulation of complex values. The VLDB Journal, 4:727#794, 1995.

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S. Abiteboul and C. Beeri. The power of languages for the manipulation of complex values. The VLDB Journal, 4#4#:727#794, October 1995.

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