## Constraint Query Languages (1992)

### Cached

### Download Links

- [www.cs.brown.edu]
- [ftp.cs.brown.edu]
- [pdf.aminer.org]
- [cse.unl.edu]
- DBLP

### Other Repositories/Bibliography

Citations: | 347 - 35 self |

### BibTeX

@MISC{Kanellakis92constraintquery,

author = {Paris C. Kanellakis and Gabriel M. Kuper and Peter Z. Revesz},

title = {Constraint Query Languages},

year = {1992}

}

### Years of Citing Articles

### OpenURL

### Abstract

We investigate the relationship between programming with constraints and database query languages. We show that efficient, declarative database programming can be combined with efficient constraint solving. The key intuition is that the generalization of a ground fact, or tuple, is a conjunction of constraints over a small number of variables. We describe the basic Constraint Query Language design principles and illustrate them with four classes of constraints: real polynomial inequalities, dense linear order inequalities, equalities over an infinite domain, and boolean equalities. For the analysis, we use quantifier elimination techniques from logic and the concept of data complexity from database theory. This framework is applicable to managing spatial data and can be combined with existing multidimensional searching algorithms and data structures.

### Citations

11243 |
Computers and Intractability: A Guide to the Theory of NP-completeness
- Garey, Johnson
- 1979
(Show Context)
Citation Context ...nd letting the database grow, we can prove that the evaluation can be performed in PTIME or in NC or in LOGSPACE, depending on the constraints that we consider (for the various complexity classes see =-=[21]-=-). (2) Let us motivate these design principles by a very common task from computational geometry and spatial databases; the problem of computing all rectangle intersections [43, 49]. Note that the the... |

1881 |
Foundations of Logic Programming
- Lloyd
- 1987
(Show Context)
Citation Context ...er expresses exactly PTIME (Section 3.1). 4. For Datalog with dense linear order constraints, we develop a bottom-up evaluation method that is closer to the classical foundations of logic programming =-=[38]-=- and knowledge bases [54, 55] (Section 3.2). This allows us to show that piecewise linear Datalog with dense linear order constraints can be evaluated bottom-up in closed form and NC data complexity (... |

1807 |
Computational Geometry: An Introduction
- Preparata, Shamos
- 1985
(Show Context)
Citation Context ...complexity classes see [21]). (2) Let us motivate these design principles by a very common task from computational geometry and spatial databases; the problem of computing all rectangle intersections =-=[43, 49]-=-. Note that the theory of constraints used in this simple, but very common, example is the theory of dense linear order with constants (see Section 3). s (a1 ;b 1 ) s (c 1 ;b 1 ) s (a1 ;d 1 ) s (c 1 ;... |

1209 |
The design and analysis of spatial data structures
- Samet
- 1990
(Show Context)
Citation Context ...anguages. (2) The possible applications of constraint databases include both data processing and numerical processing of spatial data. (3) The implementation technology of spatial access methods (see =-=[48, 49]-=-) naturally matches the new formalism. We will now explain our new framework and give arguments in support of the above (1-3). - OE(db, constraints) - . . . . . . query program database output databas... |

584 | Ubiquitous B-tree
- COMER
- 1979
(Show Context)
Citation Context ...ry efficient use of secondary storage is an additional requirement, beyond low data complexity, whose satisfaction greatly contributes to relational technology. B-trees and their variants B + -trees, =-=[5, 18]-=-, are examples of important data structures for implementing relational databases. In particular, let each secondary memory access transmit B units of data, let r be a relation with N tuples, and let ... |

579 |
A Decision Method for Elementary Algebra and Geometry
- Tarski
(Show Context)
Citation Context ...ional space D k ). ffl The syntax of a CQL is the union of an existing database query language and a decidable logical theory. For example: Relational calculus [15] + the theory of real closed fields =-=[53]-=- (Section 2); Inflationary Datalog : [1, 22, 33] + the theory of dense linear order with constants (Section 3); Inflationary Datalog : + the theory of equality on an infinite domain with constants (Se... |

538 |
The complexity of relational query languages
- Vardi
- 1982
(Show Context)
Citation Context .... A key intuition comes from Constraint Logic Programming: a conjunction of constraints is the correct generalization of the ground fact. The technical tools for this integration are: data complexity =-=[11, 60]-=- from database theory, and quantifier elimination methods from mathematical logic. Let us provide some motivation for the integration of database and constraint solving methods. Manipulation of spatia... |

330 |
A relational model for large shared data banks
- Codd
- 1970
(Show Context)
Citation Context ...e and application has been "loose". For an example of "tight" integration of application, language paradigm, and implementation, let us review the relational data model. In the rel=-=ational data model, [15]-=-, an important application area (data processing) is described in a declarative style (relational calculus) so that it can be automatically and efficiently translated into procedural style (relational... |

293 |
An introduction to Prolog-III
- Colmerauer
- 1990
(Show Context)
Citation Context ...ying how these computations are constrained [7, 36, 52]. A major recent development in logic programming systems is the integration of logic and constraint paradigms, e.g., in CLP [27], in Prolog III =-=[17]-=-, and in CHIP [19], for a recent survey see [16]. One intuitive reason for this successful integration is as follows. A strength of Prolog is its top-down, depth-first search strategy. The operation o... |

277 |
Principles of Database Systems
- Ullman
- 1982
(Show Context)
Citation Context ...he relational model is that relations are finite structures, and queries are supposed to preserve this finiteness. This is a requirement that creates various "safety" problems in relational =-=databases [15, 54]-=-. The precise analogue in relational databases is the notion of weak safety of [3]. In our framework, it is finiteness of representation of constraints that must be preserved. Evaluation of a query co... |

273 | Relational queries computable in polynomial time
- Immerman
- 1986
(Show Context)
Citation Context ... to combine them with relational calculus, but not with recursive formalisms. (b) Dense linear order constraints are also very general, since one may use them to simulate any PTIME computation (as in =-=[26]-=- and [60]). We devote a large part of our analysis to this case, because it best illustrates the desired integration with relational calculus and various recursive formalisms. Discrete linear order is... |

246 | Structure and Complexity of Relational Queries
- Chandra, Harel
- 1982
(Show Context)
Citation Context .... A key intuition comes from Constraint Logic Programming: a conjunction of constraints is the correct generalization of the ground fact. The technical tools for this integration are: data complexity =-=[11, 60]-=- from database theory, and quantifier elimination methods from mathematical logic. Let us provide some motivation for the integration of database and constraint solving methods. Manipulation of spatia... |

205 |
The Programming Language Aspects of Thinglab; a ConstraintOriented Simulation Laboratory
- Borning
- 1981
(Show Context)
Citation Context ...nd Framework Q: What's in a tuple? A: Constraints. Constraint programming paradigms are inherently "declarative", since they describe computations by specifying how these computations are co=-=nstrained [7, 36, 52]-=-. A major recent development in logic programming systems is the integration of logic and constraint paradigms, e.g., in CLP [27], in Prolog III [17], and in CHIP [19], for a recent survey see [16]. O... |

192 |
Concurrent constraint programming languages. Doctoral Dissertation Award and Logic Programming Series
- Saraswat
- 1992
(Show Context)
Citation Context ...ming paradigms are currently attracting a great deal of attention in languages for operations research applications [58, 59] and have also impacted the field of concurrent programming language design =-=[50]-=-. The use of constraints for operations research and for concurrency is sometimes semantically different from their use in our framework. For example: Constraints can be used to represent the many pos... |

178 |
Priority search trees
- McCreight
- 1985
(Show Context)
Citation Context ...This is a well-known problem with many elegant solutions from computational geometry [43]. It is a special case of 2-dimensional searching in relational databases, called 1.5-dimensional searching in =-=[41]-=-. For example, the priority search trees of [41] are a linear space data structure with logarithmic-time update and search algorithms for in-core processing. Grid-files, R-trees, and quad-trees have a... |

174 |
On the computational complexity and geometry of the first-order theory of the reals, part 1
- Renegar
- 1992
(Show Context)
Citation Context ...be used to speed-up CQL evaluation strategies? (2) The technology of algorithms for logical theories is still rather complex, but much progress has been accomplished in recent years. For example, see =-=[45]-=- for the state-of-the-art in real closed fields. Are there interesting special cases, for which simple algorithmic techniques can be used? These would be analogous to the special treatment of project-... |

172 |
Elementary induction on abstract structures
- Moschovakis
- 1974
(Show Context)
Citation Context ...ions. We will use the term unrestricted relation for finite or infinite sets of points in a k-dimensional space. It is possible to develop query languages using such unrestricted relations (e.g., see =-=[39]-=-). In order to be able to do something useful with such unrestricted relations, we need a finite representation that we can manipulate. This is exactly what the generalized tuples provide. Definition ... |

140 |
On conjunctive queries containing inequalities
- Klug
- 1988
(Show Context)
Citation Context ...n found to be particularly useful in databases and have been examined in depth. Tableaux query programs form such a fragment. We provide definitions and examples for them in Section 2.2, and refer to =-=[2, 12, 32, 54]-=- for a more detailed treatment. Complexity: We assume familiarity with the definitions of basic complexity classes such as LOGSPACE, PTIME, NC, and \Pi p 2 (see [21]). The prototypical logspace-comple... |

119 |
The complexity of elementary algebra and geometry
- Ben-Or, Kozen, et al.
- 1986
(Show Context)
Citation Context ... closed PTIME PTIME In more detail: 1. Relational calculus with real polynomial inequality constraints can be evaluated bottomup in closed form and NC data complexity. This is a direct consequence of =-=[6, 35, 53]-=- and illustrates the potential applicability of the framework to spatial databases (Section 2.1). 2. As part of our analysis of the relational calculus and real polynomial inequality constraints, we p... |

119 | Magic templates: A spellbinding approach to logic programs
- Ramakrishnan
- 1988
(Show Context)
Citation Context ...g. There has been some previous database research on the power of constraints for the implicit specification of temporal data [14], for extending relational algebra [23], and for magic set evaluation =-=[44]-=- but no overall design principles. Also, manipulation of constraints has been used to study termination properties of logic programs. For an example related to the frameworks of this paper see [8]. Th... |

108 |
Elements of Relational Database Theory
- Kanellakis
- 1990
(Show Context)
Citation Context ...lus + constraints: We present a short but self-contained description of the relational calculus with a given a class of constraints. For more details on the relational calculus in database theory see =-=[15, 29, 54]-=-. Definition 1.6 Let \Phi be a class of constraints. Let R 1 ; : : : ; R i ; : : : be predicate symbols, each with a fixed arity. A relational calculus + \Phi query program is a formula of the first-o... |

94 | Constraint Logic Programming Languages - Cohen - 1990 |

81 |
Fixed-point extensions of first-order logic
- Gurevich, Shelah
- 1986
(Show Context)
Citation Context ...L is the union of an existing database query language and a decidable logical theory. For example: Relational calculus [15] + the theory of real closed fields [53] (Section 2); Inflationary Datalog : =-=[1, 22, 33]-=- + the theory of dense linear order with constants (Section 3); Inflationary Datalog : + the theory of equality on an infinite domain with constants (Section 4); and Datalog + boolean equations (Secti... |

80 |
Equivalences among relational expressions
- Aho, Sagiv, et al.
- 1979
(Show Context)
Citation Context ...n found to be particularly useful in databases and have been examined in depth. Tableaux query programs form such a fragment. We provide definitions and examples for them in Section 2.2, and refer to =-=[2, 12, 32, 54]-=- for a more detailed treatment. Complexity: We assume familiarity with the definitions of basic complexity classes such as LOGSPACE, PTIME, NC, and \Pi p 2 (see [21]). The prototypical logspace-comple... |

75 |
Why not negation by fixpoint
- Kolaitis, Papadimitriou
- 1991
(Show Context)
Citation Context ...L is the union of an existing database query language and a decidable logical theory. For example: Relational calculus [15] + the theory of real closed fields [53] (Section 2); Inflationary Datalog : =-=[1, 22, 33]-=- + the theory of dense linear order with constants (Section 3); Inflationary Datalog : + the theory of equality on an infinite domain with constants (Section 4); and Datalog + boolean equations (Secti... |

71 |
The definition and implementation of a computer programming language based on constraints
- STEELE
- 1980
(Show Context)
Citation Context ...nd Framework Q: What's in a tuple? A: Constraints. Constraint programming paradigms are inherently "declarative", since they describe computations by specifying how these computations are co=-=nstrained [7, 36, 52]-=-. A major recent development in logic programming systems is the integration of logic and constraint paradigms, e.g., in CLP [27], in Prolog III [17], and in CHIP [19], for a recent survey see [16]. O... |

67 | Handling Infinite Temporal Data
- Kabanza, Stevenne, et al.
- 1995
(Show Context)
Citation Context ...strength of Prolog is its top-down, depth-first search strategy. The operation of first-order term unification, at the forefront of this A preliminary version of the results in this paper appeared in =-=[28]-=-. y Brown University, Providence, RI. Research was supported by IBM, by an Alfred P. Sloan Fellowship, and by ONR grants N00014-83-K-0146 ARPA Order No. 4786 and N00014-91-J-4052 ARPA Order No. 8225. ... |

61 |
Procedural and declarative database update languages (Extended Abstract
- Abiteboul, Vianu
- 1988
(Show Context)
Citation Context ...L is the union of an existing database query language and a decidable logical theory. For example: Relational calculus [15] + the theory of real closed fields [53] (Section 2); Inflationary Datalog : =-=[1, 22, 33]-=- + the theory of dense linear order with constants (Section 3); Inflationary Datalog : + the theory of equality on an infinite domain with constants (Section 4); and Datalog + boolean equations (Secti... |

51 | Pushing Constraint Selections
- Srivastava, Ramakrishnan
- 1993
(Show Context)
Citation Context ...hould be investigated in a CQL framework. (3) How do various optimization methods combine with our framework? This would involve extending [44]. For some recent research in this direction we refer to =-=[24, 37, 42, 51]-=-. Constraint manipulation for database logic program analysis is also related to optimization, e.g., [8, 9, 57]. (4) Constraint query languages should be designed in an extendible way. For example, th... |

49 |
der Meyden. The Complexity of Querying Indefinite Information: Defined relations, Recursion and Linear Order
- van
- 1992
(Show Context)
Citation Context ... temporal databases we refer to [4, 13, 28]. In Section 2.2, we left open the complexity of tableau containment with dense linear order inequalities. This has been recently shown \Pi p 2 -complete in =-=[56]. It would-=- be very interesting to study the implementation of the "declarative and efficiently evaluable" languages outlined in this paper. The results presented here should be properly viewed as posi... |

47 |
A Closed Form for Datalog Queries with Integer Order
- Revesz
- 1990
(Show Context)
Citation Context ...he development of analogous frameworks for the theory of discrete linear order with constants, e.g., see [28]. For recent developments of constraint-based approaches to temporal databases we refer to =-=[4, 13, 46]-=-. Our results on linear order only apply to dense linear order. The case of discrete, or integer, linear order is analyzed in [46]. 2 Remark B: The key concept in CQL, illustrated by Example 1.1, is t... |

42 | On the representation of infinite temporal data and queries
- Baudinet, Niezette, et al.
- 1991
(Show Context)
Citation Context ...he development of analogous frameworks for the theory of discrete linear order with constants, e.g., see [28]. For recent developments of constraint-based approaches to temporal databases we refer to =-=[4, 13, 46]-=-. Our results on linear order only apply to dense linear order. The case of discrete, or integer, linear order is analyzed in [46]. 2 Remark B: The key concept in CQL, illustrated by Example 1.1, is t... |

39 |
Embedding boolean expressions into logic programming
- Büttner, Simonis
- 1987
(Show Context)
Citation Context ...oach to safe queries of [3, 25, 31, 44] (Section 4). 6. Finally, Datalog with boolean equality constraints can be evaluated bottom-up and in closed form. For the definitions we refer to Section 5 and =-=[10, 34, 40]-=-. The data complexity here is higher than in the previous cases and it depends on the use of free boolean algebras with m generators. We partly analyze this data complexity and show it to be \Pi p 2 -... |

36 | Deriving constraints among argument sizes in logic programs
- Gelder
- 1991
(Show Context)
Citation Context ...uld involve extending [44]. For some recent research in this direction we refer to [24, 37, 42, 51]. Constraint manipulation for database logic program analysis is also related to optimization, e.g., =-=[8, 9, 57]-=-. (4) Constraint query languages should be designed in an extendible way. For example, this would make it possible to integrate a select set of computational geometry algorithms as primitives in a bot... |

35 |
Organization of large ordered indexes
- Bayer, McCreight
- 1972
(Show Context)
Citation Context ...ry efficient use of secondary storage is an additional requirement, beyond low data complexity, whose satisfaction greatly contributes to relational technology. B-trees and their variants B + -trees, =-=[5, 18]-=-, are examples of important data structures for implementing relational databases. In particular, let each secondary memory access transmit B units of data, let r be a relation with N tuples, and let ... |

35 |
Constraint programming languages
- Leler
- 1988
(Show Context)
Citation Context ...nd Framework Q: What's in a tuple? A: Constraints. Constraint programming paradigms are inherently "declarative", since they describe computations by specifying how these computations are co=-=nstrained [7, 36, 52]-=-. A major recent development in logic programming systems is the integration of logic and constraint paradigms, e.g., in CLP [27], in Prolog III [17], and in CHIP [19], for a recent survey see [16]. O... |

33 |
Parallel complexity of logical query programs
- Ullman, Gelder
- 1986
(Show Context)
Citation Context ...E (Section 3.1). 4. For Datalog with dense linear order constraints, we develop a bottom-up evaluation method that is closer to the classical foundations of logic programming [38] and knowledge bases =-=[54, 55]-=- (Section 3.2). This allows us to show that piecewise linear Datalog with dense linear order constraints can be evaluated bottom-up in closed form and NC data complexity (Section 3.3). 5. Relational c... |

32 |
Inference of monotonicity constraints in Datalog programs
- Brodsky, Sagiv
- 1989
(Show Context)
Citation Context ...on [44] but no overall design principles. Also, manipulation of constraints has been used to study termination properties of logic programs. For an example related to the frameworks of this paper see =-=[8]-=-. The main contribution of this paper is to show that it is possible to bridge the gap between: bottom-up, efficient, declarative database programming and efficient constraint solving. A key intuition... |

32 |
Optimal Implementation of Conjunctive Queries
- Chandra, Merlin
- 1977
(Show Context)
Citation Context ...n found to be particularly useful in databases and have been examined in depth. Tableaux query programs form such a fragment. We provide definitions and examples for them in Section 2.2, and refer to =-=[2, 12, 32, 54]-=- for a more detailed treatment. Complexity: We assume familiarity with the definitions of basic complexity classes such as LOGSPACE, PTIME, NC, and \Pi p 2 (see [21]). The prototypical logspace-comple... |

27 |
Complexity of Boolean Algebras
- Kozen
- 1980
(Show Context)
Citation Context ...oach to safe queries of [3, 25, 31, 44] (Section 4). 6. Finally, Datalog with boolean equality constraints can be evaluated bottom-up and in closed form. For the definitions we refer to Section 5 and =-=[10, 34, 40]-=-. The data complexity here is higher than in the previous cases and it depends on the use of free boolean algebras with m generators. We partly analyze this data complexity and show it to be \Pi p 2 -... |

25 |
Relational specifications of infinite query answers
- Chomicki, Imielinski
- 1993
(Show Context)
Citation Context ...dict the top-down, depthfirst intuition behind Constraint Logic Programming. There has been some previous database research on the power of constraints for the implicit specification of temporal data =-=[14]-=-, for extending relational algebra [23], and for magic set evaluation [44] but no overall design principles. Also, manipulation of constraints has been used to study termination properties of logic pr... |

23 | Polynomial time query processing in temporal deductive databases
- Chomicki
- 1990
(Show Context)
Citation Context ...he development of analogous frameworks for the theory of discrete linear order with constants, e.g., see [28]. For recent developments of constraint-based approaches to temporal databases we refer to =-=[4, 13, 46]-=-. Our results on linear order only apply to dense linear order. The case of discrete, or integer, linear order is analyzed in [46]. 2 Remark B: The key concept in CQL, illustrated by Example 1.1, is t... |

22 | Domain independence and the relational calculus
- Hull, Su
- 1994
(Show Context)
Citation Context ...Inflationary Datalog : ) with equality constraints over an infinite domain can be evaluated bottom-up in closed form and LOGSPACE (PTIME) data complexity. This extends the approach to safe queries of =-=[3, 25, 31, 44]-=- (Section 4). 6. Finally, Datalog with boolean equality constraints can be evaluated bottom-up and in closed form. For the definitions we refer to Section 5 and [10, 34, 40]. The data complexity here ... |

21 |
Reduction of a relational model with infinite domains to the finite-domain case
- Ailamazyan, Gilula, et al.
- 1986
(Show Context)
Citation Context ...o preserve this finiteness. This is a requirement that creates various "safety" problems in relational databases [15, 54]. The precise analogue in relational databases is the notion of weak =-=safety of [3]-=-. In our framework, it is finiteness of representation of constraints that must be preserved. Evaluation of a query corresponds to an instance of a decision problem. Interestingly, many quantifier eli... |

18 |
On safety, domain independence, and capturability of database queries
- Kifer
- 1988
(Show Context)
Citation Context ...Inflationary Datalog : ) with equality constraints over an infinite domain can be evaluated bottom-up in closed form and LOGSPACE (PTIME) data complexity. This extends the approach to safe queries of =-=[3, 25, 31, 44]-=- (Section 4). 6. Finally, Datalog with boolean equality constraints can be evaluated bottom-up and in closed form. For the definitions we refer to Section 5 and [10, 34, 40]. The data complexity here ... |

16 |
Unification in Boolean Rings
- Martin, Nipkow
- 1988
(Show Context)
Citation Context ...oach to safe queries of [3, 25, 31, 44] (Section 4). 6. Finally, Datalog with boolean equality constraints can be evaluated bottom-up and in closed form. For the definitions we refer to Section 5 and =-=[10, 34, 40]-=-. The data complexity here is higher than in the previous cases and it depends on the use of free boolean algebras with m generators. We partly analyze this data complexity and show it to be \Pi p 2 -... |

14 | Constraint-based Query Optimization for Spatial Databases
- Helm, Marriott, et al.
- 1991
(Show Context)
Citation Context ...hould be investigated in a CQL framework. (3) How do various optimization methods combine with our framework? This would involve extending [44]. For some recent research in this direction we refer to =-=[24, 37, 42, 51]-=-. Constraint manipulation for database logic program analysis is also related to optimization, e.g., [8, 9, 57]. (4) Constraint query languages should be designed in an extendible way. For example, th... |

12 |
An efficient decision procedure for the theory of rational order
- Ferrante, Geiser
- 1977
(Show Context)
Citation Context ...elational calculus (Inflationary Datalog : ) with dense linear order constraints can be evaluated bottom-up in closed form and LOGSPACE (PTIME) data complexity. This is shown by adapting the proof of =-=[20]-=-. Also, by a slight modification of [26, 60] Inflationary Datalog : with dense linear order expresses exactly PTIME (Section 3.1). 4. For Datalog with dense linear order constraints, we develop a bott... |

10 | A logic language for combinatorial optimization
- Hentenryck
- 1990
(Show Context)
Citation Context ...objects. Our framework is thus one of complete information. Constraint logic programming paradigms are currently attracting a great deal of attention in languages for operations research applications =-=[58, 59]-=- and have also impacted the field of concurrent programming language design [50]. The use of constraints for operations research and for concurrency is sometimes semantically different from their use ... |

5 |
Algebraic cell decomposition
- Kozen, Yap
- 1985
(Show Context)
Citation Context ... closed PTIME PTIME In more detail: 1. Relational calculus with real polynomial inequality constraints can be evaluated bottomup in closed form and NC data complexity. This is a direct consequence of =-=[6, 35, 53]-=- and illustrates the potential applicability of the framework to spatial databases (Section 2.1). 2. As part of our analysis of the relational calculus and real polynomial inequality constraints, we p... |