Paris C. Kanellakis, Gabriel M. Kuper, and Peter Z. Revesz. Constraint query languages. Journal of Computer and System Sciences, 51(1):26--52, August 1995. Preliminary version appeared in Proceedings of the 9th ACM Symposium on Principles of Database Systems (PODS), 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....: D n are arbitrary domains. The idea of using the duality between constraints and sets of points they define in programming systems goes to constraint logic programming (e.g. JaL87] The MDS objects we study here are strongly related to, and contain as a subfamily, generalized relations in [KKR90] and CST objects using linear constraints over reals in [BK95] that we used in the motivating example) 7.1 Constraint Formulae vs. Multidimensional Sets Although MDS objects represent infinite sets, they, clearly, must be finitely representable. The finite representation of MDS will be by ....

P. Kanellakis, G. Kuper, P. Revesz, Constraint Query Languages, J. Computer and System Sciences, to appear. (A preliminary version appeared in Proc. 9th PODS, 299--313, 1990.)

....of N constraint relations. The spatial interpretation of the constraint join is the spatial intersection R 1 : RN . We consider the case where the space dimension d is bounded, while the number of relations N , and the number of tuples in each relation can grow. Within the CQL framework of [KKR90] this problem is considered for the case when the query size is xed (i.e. when N is bounded) which guarantees a polynomial CPU evaluation. A similar problem has been examined in spatial databases, where it is referred to as the multiway spatial join. It is interesting that, while the binary ....

....= 1; N . If no misinterpretation arises, we will also use the term N combination to denote the conjunction t 1 : t N . We call an N combination non empty if the conjunction is satis able (i.e. the corresponding spatial intersection is not empty) The existing evaluation methods ([KKR90, PM99, MP99]) do not guarantee polynomiality in the general case. Those methods compute the result as a union of all the non empty N combinations. However, situations are possible when the number of all the non empty N combinations is exponential in N . Indeed, consider a set of tuples from [ N i=1 R i ....

P. Kanellakis, G. Kuper, and P. Revesz. Constraint query languages. J. Computer and System Sciences, to appear. (A preliminary version appeared in Proc. 9th PODS, pages 299-313, 1990.

....Constraint representation is DISCO is useful in many, but not all applications. For example, to express satisfiability of a simple propositional formula, the user needs to encode the formula by a datalog (with constraints) program, in a fairly unnatural way. Close to the other end, the framework [KKR90] requires a fairly restricted sub family of first order logic in constraint objects: disjunction of (unquantified) conjunctions of atomic constraints (the algebra, however, allows more, including quantifier elimination) This representation is useful for many, but not all applications: for ....

....space, 2) have query languages restricted to predefined spatio temporal operators, and (3) lack global economical filtering and deep optimization. There has been work on the use of constraints in databases, earlier of which include [Klu88, HHLvEB, CI89, Ram91, BS89] The pioneering work [KKR90] proposed a framework for integrating abstract constraints into database query languages by providing a number of design principles, and studied, mostly in terms of expressiveness and complexity, a number of specific instances. The work [HHLvEB] considered polynomial equality constraints, ....

P. Kanellakis, G. Kuper, and P. Revesz. Constraint query languages. J. Computer and System Sciences, to appear. (A preliminary version appeared in Proc. 9th PODS, pages 299--313, 1990.

....problem for CGDs and two classes of CGDs with polynomial time solution of their implication problem. CFDs have several applications to query processing in constraint logic programming (CLP) languages and constraint databases (CDBs) where data is represented by constraints (see, for example, [21]) as well as conventional relational and deductive databases. We investigate in detail a subsumption analysis which takes advantage of the extra power of CFDs. This analysis, which generalizes the analysis of [27] can be used to omit unnecessary subsumption tests in bottom up execution and to ....

....to test whether one constraint implies another. The way a relation is defined is not relevant to the results of this paper, although it might be relevant to their application. For concreteness, we have in mind relations defined through constraints by (possibly infinitely many) generalized tuples [21], relations defined by formulas which are not constraints (for example, z = maxfx y; x yg) and the composition of these by conjunction and disjunction. This class includes those relations defined by CLP programs and CDB queries. 3 Constrained Dependencies A constrained dependency generalizes ....

P. Kanellakis, G. Kuper & P. Revesz, Constraint Query Languages, Journal of Computer and System Sciences, to appear. Preliminary version appeared in Proc. 9th ACM Symp. on Principles of Database Systems, 299--313, 1990.

....Computation Bottom up execution computes (a representation of) the least model lm(P; D) associated with a program P . In many cases, and particularly for database applications, a central condition on the constraint domain is that that bottomup evaluation terminate, for all programs and queries [13]. Such a condition would severely restrict possible constraint domains for use with recursive queries. Fortunately, analysis and transformation techniques can guarantee termination of queries in many cases, even when the least model of the original program cannot be represented explicitly and ....

....that r 2 does not subsume r 1 . Nevertheless, T D r 1 T D r 2 . 2 We can attribute the discrepancy in the above example to the existence of more than one rule mapping from r 2 to r 1 . Once all rule mappings are taken into account, the discrepancy disappears. The following lemma is proved in [13] for a particular constraint domain and a single subsuming rule. That proof extends easily to the general case. We phrase the extended result in the terminology we have established. Lemma 4.10 Let r i be the rule h c i ; B i over constraint domain (D; L) for i = 0; 1; n. Let P = fr 1 ; ....

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P. Kanellakis, G. Kuper & P. Revesz, Constraint Query Languages, Journal of Computer and System Sciences, to appear. Preliminary version appeared in Proc. 9th PODS, 299--313, 1990.

....in Lin is given in [236] Some work avoids the problem of subsumption by allowing only ground facts in the database and intermediate computations. Even with subsumption, there is still the problem that execution might not terminate (for example, if P is not finitary) The approach of [144] is to restrict the constraint domains D to those which only permit the computation of finitely representable relations from finitely representable relations. This requirement is slightly weaker than requiring that all programs are finitary, but it is not clear that there is a practical ....

....program terminates [151, 211, 35] although most work has ignored the capability of using constraints in the answers. Comparatively little work has been done on the nuts and bolts of implementing bottom up execution for CLP programs, with all the work addressing the constraint domain Lin . [144] suggested the use of intervals, computed as the projection of a collection of constraints, as the basis for indexing on constrained variables. Several different data structures, originally developed for spatial databases or computational geometry, have been proposed as appropriate for indexing ....

[Article contains additional citation context not shown here]

P. Kanellakis, G. Kuper & P. Revesz, Constraint Query Languages, Journal of Computer and System Sciences, to appear. Preliminary version appeared in Proc. 9th ACM Symp. on Principles of Database Systems, 299--313, 1990.

....: D n are arbitrary domains. The idea of using the duality between constraints and sets of points they define in programming systems goes to constraint logic programming (e.g. JaL87] The MDS objects we study here are strongly related to, and contain as a subfamily, generalized relations in [KKR90] and CST objects using linear constraints over reals in [BK95] that we used in the motivating example) 11 . 7.1 Constraint Formulae vs. Multidimensional Sets Although MDS objects represent infinite sets, they, clearly, must be finitely representable. The finite representation of MDS will be ....

P. Kanellakis, G. Kuper, P. Revesz, Constraint Query Languages, J. Computer and System Sciences, to appear. (A preliminary version appeared in Proc. 9th PODS, 299--313, 1990.)

....Linear Constraint DataBases: What and Why LyriC [BK95] is a data model and language for querying object oriented databases where objects hold spatial, temporal or constraint data, conceptually represented by equality and inequality constraints. LyriC extends flat constraint query languages [KR93], especially those for linear constraint databases [BJM93] to structurally complex objects. The extension is based on the object oriented paradigm, where constraints are treated as first class objects that are organized in classes. The query language is an extension of the language XSQL [KKS92] ....

....languages, and (3) lack global economical filtering and deep optimization, interleaving the approximations and indexing of (CST like) object with the optimization engine. There has been work on the use of constraints in databases, earlier of which include [Kl88, HHLV, CI89, R91, BS89] The work [KR93] introduced a framework for integrating abstract constraints into (flat) database query languages by providing a number of design principles, and studied expressibility and complexity issues of specific instances of the framework. The work [HHLV] considered more than just linear constraints (but ....

P. Kanellakis, G. Kuper, P. Revesz, Constraint Query Languages, J. Computer and System Sciences, to appear. (A preliminary version appeared in Proc. 9th PODS, 299-313, 1990.)

....list of the variables that may be used to express constraints assigned to these attributes. These are used in order to allow for the possibility of jointly constraining different attributes when they are operated on together by constraint operations. LyriC extends flat constraint query languages [KKR93], especially those for linear constraint databases [BJM93] by incorporating constraints as a basic tool for describing spatio temporal information in constraint databases. The LyriC model treats each constraint object separately, instead of viewing each constraint tuple as a conjunction of all ....

....operation in a query. Integrating constraints as another means of description of objects within an object oriented data model is a natural requirement for supporting larger and more complex applications with constraint technology. Existing proposals for flat relational constraints databases [KKR93, BJM93], have the same problems in supporting complex spatio temporal applications that standard relational systems have [KLW90] The LyriC query language is a superset of XSQL [KKS92] suggested by Kifer, Kim and Sagiv, as an extension of SQL to object oriented databases, and is built around the idea of ....

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P. Kanellakis, G. Kuper, P. Revesz, Constraint Query Languages, Journal of Computer and System Sciences, to appear. (A preliminary version appeared in Proc. 9th PODS, 299--313, 1990.)

....into Datalog C over tractable constraint domains. We also use Datalog C to analyze another prominent TM systems KeyNote [3] and show that KeyNote uses constraint domains that are too expressive. Constraint Datalog has been studied extensively in the Constraint Database (CDB) literature [11, 12, 18 21]. However, TM applications involve constraint domains that are outside the scope of previous CDB research. Moreover, TM applications have di#erent computational complexity requirements. In the CDB literature, tractability is often measured using data complexity, which considers the processing time ....

....of variables per rule, construction of its minimal model takes time polynomial in the size of the program. 4. There are e#cient goal directed evaluation procedures for answering queries. 3 2. 2 Constraint Domains and Constraint Databases The notion of constraint databases was introduced in [11], and grew out of the research on Datalog and CLP. It generalizes the relational model of data by allowing infinite relations that are finitely representable using constraints. Constraint databases find many applications in spatial and temporal databases. For recent surveys, see [12, 18] ....

[Article contains additional citation context not shown here]

Paris C. Kanellakis, Gabriel M. Kuper, and Peter Z. Revesz. Constraint query languages. Journal of Computer and System Sciences, 51(1):26--52, August 1995. Preliminary version appeared in Proceedings of the 9th ACM Symposium on Principles of Database Systems (PODS), 1990.

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