J. Van den Bussche, D. Van Gucht, M. Andries, and M. Gyssens. On the Completeness of Object Creating Query Languages. In Proceedings FOCS-92, pp. 372--379, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....by exhibiting queries (cf. the end of this section) which can be expressed in disjunctive datalog but not in standard DATALOG 6= unless the polynomial hierarchy collapses. Our results complement and extend previous studies of important extensions of datalog and related query languages (cf. [CH85, Van87, KV90, ASV90, AV91, KP91, HS91, VVAG92] and many others [Kan90] Due to space limitations, we will comment on these extensions in the full paper. We only note that all major versions of DATALOG 6= KP91, Sch90, vRS91] express database queries in NP(resp. co NP) Thus, disjunction adds expressive power (unless Sigma P 2 = NP) ....

J. Van den Bussche, D. Van Gucht, M. Andries, and M. Gyssens. On the Completeness of Object Creating Query Languages. In Proceedings FOCS-92, pp. 372--379, 1992.

.... built using the set and tuple constructors to allow for recursive types. Unbounded value structures can thus be defined, essentially corresponding to hereditarely finite sets. The connection between hereditarely finite set construction and value invention was shown by Van den Bussche et al.[37], which reconciled the two approaches. The idea of value invention originates from a proposal by Kuper and Vardi [31, 32] to choose arbitrary symbolic object names to manage new complex object values defined in their logical queries. The concept of object name is a refinement of Codd s notion of ....

....wILOG : with unbounded stratified negation) to express the computable queries can be inferred from [22] There, the results refer to COL, a rule based language with stratified negation and untyped set construction. The two approaches are comparable, as it is suggested by Van den Bussche et al. [37], where value invention is related to 30 hereditarely finite set construction. However, COL programs have to be stratified with respect to set construction as well; furthermore, negation in COL can be simulated using set construction [1] because of this, it is not clear whether the results ....

[Article contains additional citation context not shown here]

J. Van den Bussche, D. Van Gucht, M. Andries, and M. Gyssens. On the completeness of object-creating query languages. In 33rd Annual Symp. on Foundations of Computer Science, pages 372--379, 1992.

....3 graphs with 3 arrows between 2 arrows and so on. It is worth noting that the 2 graph based logic is implicitly used in the relational database theory in considerations involving permutations of value domain elements (eg, in issues related to Paredaens notion of query language completeness ([29]) and the like) To treat the issue in the arrow style, one should introduce 2 arrows between functions: given two parallel functions f; g : A B, a 2 arrow between them is defined to be a pair (ff; fi) where ff is a permutation of A and fi is a permutation of B such that ff. f = g. fi (see [11] ....

J. Van den Bussche, D. Van Gutch, M. Andries, and M. Gyssens. On the completeness of object-creating query languages. In 33rd Symposium on Foundations of Computer Science,

....them so that an extent of a given sketch S is a graph morphism : jSj N U . Of course, to provide sufficient richness of the graph U one should presuppose that the universe Obj possesses some closure properties: closedness under hereditary finite sets, Obj = HF(Obj ) would be sufficient (cf. [40, 36]) ii) Semantics of a marker P is defined to be a mapping [ P ] Gra(Shp(P ) U ) ftrue; falseg: In addition, if one makes a reasonable assumption that urelements are uninterpreted abstract objects, then diagram predicates should not depend on their permutations: GEN) P ] ffi ) ....

J. Van den Bussche, D. Van Gutch, M. Andries, and M. Gyssens. On the completeness of object-creating query languages. In 33rd Symposium on Foundations of Computer Science, pages 372--379, 1992.

....programmer has the possibility to work with non reduced instances, if he or she wants so. A limited number of reductions can be desirable for efficiency reasons. Theorem 3.1 PaMaL is computationally complete. Proof We can simulate GOOD, which is proved to be computationally complete [GPVdBVG92, VdBVGAG92] The technical details are omitted here. 4 Conclusion In this paper we presented a graphical object oriented database model and a graph based manipulation language. We formally explained the syntax of scheme graphs. Then we defined the syntax of instance graphs and reduced instance graphs. ....

J. Van den Bussche, D. Van Gucht, M. Andries, and M. Gyssens. On the completeness of object-creating query languages. In Proceedings 33nd Symposium on Foundation of Computer Science, pages 372--379. IEEE Computer Society Press, 1992.

....Then an extent of a given sketch S (in the context O) is a graph morphism : jSj U . Of course, to provide sufficient richness of the graph U one should presuppose that the universe O possesses some closure properties: closedness under hereditary finite sets, O = HFO, would be sufficient (cf. [11, 42, 36]) Definition . Semantics of a marker P i is defined to be a mapping [ P i ] S fGraMap(D;U ) D 2 Shp(P i )g ftrue; falseg: In addition, this mapping should satisfy a certain genericity condition defined in the following way. Let : O O be a permutation of proto objects, 2 Aut(O) ....

J. Van den Bussche, D. Van Gutch, M. Andries, and M. Gyssens. On the completeness of object-creating query languages. In 33rd Symposium on Foundations of Computerr Science, pages 372--379, 1992.

....with respect to determinacy stems from the fact that the definition of determinacy does not take into account that new objects in IQL are always created in terms of existing objects. Therefore, Andries and the present authors defined a more restrictive notion of query, called constructive query [23], and showed that IQL is complete with respect to the constructive queries. It should be noted that this completeness result is by no means specific to IQL, as IQL is equivalent to any minimal language that can express first order queries, object creation, and unbounded looping. Therefore, many ....

....It should be noted that this completeness result is by no means specific to IQL, as IQL is equivalent to any minimal language that can express first order queries, object creation, and unbounded looping. Therefore, many other object creating query languages that have been considered (e.g. [15, 16, 17, 19, 23]) are essentially equivalent to IQL. Extending IQL to a complete language requires the introduction of an involved determinate copy elimination mechanism [2, 13] suggesting that the concept of determinate query is perhaps less natural than originally anticipated. From this viewpoint, restricting ....

[Article contains additional citation context not shown here]

J. Van den Bussche, D. Van Gucht, M. Andries, and M. Gyssens. On the completeness of object-creating query languages. In Proc. 33rd IEEE Symp. Foundations of Computer Science, 372--379. 1992.

.... turns out that IsaLog is not computationally complete for relational transformations, in the sense that it cannot express all computable queries of [10] Consequently, with respect to the ability of expressing objectoriented queries, IsaLog is complete neither in the sense of [2] nor in that of [21]. This inability is not in contradiction with our simulation, where we have assumed some restrictions on the nature of the computations, as follows: ffl we assume the input instance to code an input string for the Turing machine in a suitable way. In the most general and usual case, the input is ....

.... negation with inflationary semantics [17, 18] it turns out that, in presence of oid invention (or an equivalent construct) stratified and inflationary negation have the same expressive power [12] We claim that IsaLog : expresses all computable queries and all the list constructive queries of [21]. A deeper analysis of the expressive power of the language will be done in a forthcoming paper [6] 5.2 Further Issues about Model Finiteness Two important properties for IsaLog programs have been studied, namely, functionality and model finiteness. The corresponding problems of deciding ....

J. Van den Bussche, D. Van Gucht, M. Andries, and M. Gyssens. On the completeness of object-creating query languages. In 33rd Annual Symp. on Foundations of Computer Science, pages 372--379, 1992.

....in a fixpoint fashion. Another proposal to achieve completeness extends the data model with complex objects built using set and tuple constructors allowing for recursive types [11] Unbounded value structures can thus be defined, essentially corresponding to hereditarely finite sets. In [16] the connection between hereditarely finite set construction and value invention is shown, and the two approaches reconciled. Query languages with value invention may allow for new values in the result of a query; we will call transformations this kind of queries, whose semantics is a binary ....

....invention may allow for new values in the result of a query; we will call transformations this kind of queries, whose semantics is a binary relation rather than a function. For transformation languages, criterions that extend genericity have been proposed (e.g. determinacy [1] and constructivism [16]) In this paper we study a family of rule based transformation languages with value invention, with semantics of invention based on Skolem functors and stratified semantics for negation. The formalism adopted is that of ILOG ( 13] which enjoys all the above characteristics, while keeping ....

[Article contains additional citation context not shown here]

J. Van den Bussche, D. Van Gucht, M. Andries, and M. Gyssens. On the completeness of object-creating query languages. In 33rd Annual Symp. on Foundations of Computer Science, pages 372--379, 1992. This article was processed using the L a T E X macro package with LLNCS style

..... 2 fa; bg = 3 Gamma Gamma Gamma Psi H H H H H Hj 0 R 1 Gamma Gamma Gamma Phi Phi Phi Phi Phi Phi 2 I oe a b Figure 2: A query not expressible in while new . There is an elegant necessary condition for a query to be computable by Datalog : new [AP92, dBGAG92] We present this condition, then show how it can be used to prove that the query in Example 7.2 is not expressible by Datalog : new . The condition involves inputoutput pairs of Datalog : new programs. For each input output pair hI; Ji, the condition requires a simple connection between ....

....a simple connection between the automorphism group of I and that of J . For an instance K, let Aut(K) denote the set of automorphisms of K. For a pair of instances K;K 0 , Aut(hK; K 0 i) denotes the bijections on adom(K [ K 0 ) that are automorphisms of both K and K 0 . Theorem 7. 3 [dBGAG92] A query q is expressible in Datalog : new only if for each inputoutput pair hI; Ji in q there exists a mapping h from Aut(I) to Aut(hI; Ji) such that for each ; 2 Aut(I) i) and h( coincide on I; ii) h( ffi ) h( ffi h( and 3 , iii) h(id I ) id hI;Ji . We note that this ....

[Article contains additional citation context not shown here]

J. Van den Bussche, D. Van Gucht, M. Andries, and M. Gyssens. On the completeness of object-creating query languages. In IEEE Conf. on Foundations of Computer Science, pages 372--379, 1992.

....and natural forms of restructuring, is complete w.r.t. our criteria. We also compare our model and language with existing ones and bring out their power and generality. Among other things, we show the following. 4) The graphbased object oriented data model GOOD recently proposed by Gyssens et al. [9, 4, 3] can be embedded within the tabular database model. In particular, every GOOD query can be expressed in the tabular algebra. This observation also provides a means to embed other models encompassed by GOOD, such as the nested and complex object models, in the tabular model. 5) The syntactic ....

J. Van den Bussche, D. Van Gucht, M. Andries, and Gyssens, M. On the completeness of objectcreating query languages. 33rd Symposium on Foundations of Computer Science, 1992.

....turns out that this query is not expressible in while new , and even in more powerful languages using complex values. To understand why, we present an elegant necessary condition in order for queries to be expressible in while new (this becomes also sufficient for certain more powerful languages) dBGAG92] For an instance K, let Aut(K) denote the set of automorphisms of K. For a pair K;K 0 of instances, Aut(hK; K 0 i) denotes the bijections on adom(K [ K 0 ) that are automorphisms of both K and K 0 . An extension homomorphism from Aut(K) to Aut(hK; K 0 i) is a mapping h : Aut(K) ....

J. Van den Bussche, D. Van Gucht, M. Andries, and M. Gyssens, On the completeness of object-creating query languages, IEEE Conf. on Foundations of Computer Science, 1992, pp. 372--379.

....must work, are described by means of a graph pattern. The operation will be applied for every matching of this pattern in the database graph. Patterns in isolation have the power of select project join queries; the operational power of full language is computationally complete, as shown in [5, 6]. To our knowledge, this is the first graphical user interface with this property. Syntactically, each operation is a graph, consisting of a pattern with special nodes and edges to indicate which nodes or edges have to be added or deleted or where duplicates have to be eliminated. The base ....

J. Van den Bussche, D. Van Gucht, M. Andries, and M. Gyssens. On the completeness of object-creating query languages. In Proceedings 33nd Symposium on Foundation of Computer Science, pages 372--379. IEEE Computer Society Press, 1992.

No context found.

J. Van den Bussche, D. Van Gucht, M. Andries, and M. Gyssens. On the completeness of object-creating query languages. In Proceedings 33rd Symposium on Foundations of Computer Science, pages 372--379. IEEE Computer Society Press, 1992.

....strong to simulate arbitrary Turing Machines; this can be shown using well known techniques (e.g. 34] Finally, on the most general level, one may ask exactly which graph transformations (i.e. computable mappings from graphs to graphs) can be expressed in GOOD. This question was addressed in [33]; informally speaking, it was shown there that GOOD can express all isomorphism preserving transformations for which newly created objects can be effectively constructed . 5 Concluding remarks We end the paper with some concluding remarks. The GOOD transformation language is reminiscent of graph ....

J. Van den Bussche, D. Van Gucht, M. Andries, and M. Gyssens. On the completeness of object-creating query languages. In Proceedings 33rd Symposium on Foundations of Computer Science, pages 372--379. IEEE Computer Society Press, 1992.

....see [1] this second requirement is equivalent with the requirement that the function preserves graph isomorphisms. A powerful language for expressing graph functions is the language provided by the GOOD model, a graph oriented model for object databases [6, 7, 5] Recently, it has been shown [10] that all generically computable graph functions of interest (in a sense which can be made precise) are expressible in GOOD. This result gave evidence that the class of GOOD graph functions serves as a yardstick for the completeness of data manipulation formalisms. Supported by the DPWB under ....

J. Van den Bussche, D. Van Gucht, M. Andries, and M. Gyssens. On the completeness of object-creating query languages. In Proceedings 33rd Symposium on Foundations of Computer Science, pages 372--379. IEEE Computer Society Press, 1992.

....that the class of determinate queries is perhaps not so natural after all. This philosophically unsatisfactory situation left open two natural directions for further research: restrict or extend the class of determinate queries to find more natural classes. The first direction was explored in [29], where the precise expressive power of IQL was characterized. It was shown that this characterization is obtained when an additional requirement, besides determinacy, is made which simply expresses that the creation of new objects can be interpreted as the deterministic construction of ....

....requirement, besides determinacy, is made which simply expresses that the creation of new objects can be interpreted as the deterministic construction of hereditarily finite sets. The feeling expressed above that the class of IQL expressible determinate queries, coined the constructive queries in [29], indeed arises very naturally was thus confirmed. In the present paper, we explore the other direction. We propose the notion of semi determinism. A non deterministic query is called semideterministic if any two different results of the query to a database are isomorphic, by an isomorphism which ....

[Article contains additional citation context not shown here]

J. Van den Bussche, D. Van Gucht, M. Andries, and M. Gyssens. On the completeness of object-creating query languages. In Proceedings 33rd Symposium on Foundations of Computer Science, pages 372--379. IEEE Computer Society Press, 1992.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC