J. Cox, K. McAloon. Decision Procedures for Constraint Based Extensions of Datalog. In: F. Benhamou, A. Colmerauer, eds., Constraint Logic Programming, MIT Press, 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....some half addition constraints are not gap order constraints. For example, x y 5 is a half addition constraint but it is not expressible by gap order constraints. A least fixpoint evaluation for Datalog with gap order constraints is described in [24] The recognition problem is also studied in [8]. The DISCO system [5] implements Datalog queries with integer gap order constraints. Adding negation in a safe way to Datalog with gap order queries is studied in [25] A temporal constraint is like a gap order constraint but the gap value can be any integer (both negative and non negative) ....

J. Cox, K. McAloon. Decision Procedures for Constraint Based Extensions of Datalog. In: F. Benhamou, A. Colmerauer, eds., Constraint Logic Programming, MIT Press, 1993.

.... for representing incomplete temporal information [31, 23] If one surveys the existing work on databases with interpreted data and implicit representations, one finds contributions on the expressiveness of the various representation formalisms [2, 5, 4] on the complexity of query evaluation [9, 12, 25, 31], and on data structures and algorithms to be used in the representation of constraint expressions and in query evaluation [28, 7, 8, 22] However, much less has been done on extending other parts of traditional database theory, for instance schema design and dependency theory. It should be clear ....

J. Cox and K. McAloon. Decision procedures for constraint based extensions of Datalog. In F. Benhamou and A. Colmerauer, editors, Constraint Logic Programming: Selected Research. MIT Press, 1993.

....addition and multiplication in terms of successor. Thus, diophantine equations can be expressed in this fragment of CLP. On the other hand, simpler constraints, namely constraints over ordered infinite domains (of some particular kind) do not increase the complexity of Datalog. Theorem 9. 2 ([34]) CLP over (Z; 0; Sigma1; Sigma2; is DEXPTIME complete. The same holds for any of Q or R instead of Z. 16 Decidable fragments of CLP over more complex structures are obtained by restrictions imposed on constraint logic programs. For example, we consider a conservative CLP in which ....

J. Cox and K. McAloon. Decision procedures for constraint-based extensions of datalog. In F. Benhamou and A. Colmerauer, editors, Constraint Logic Programming, Selected Research, pp. 17--32. The MIT Press, 1993.

.... and their (potential) applications are well treated in the literature (e.g. 47] Of special relevance to us is the fact that any implementation of such languages must understand much about the underlying mathematical domain, especially its computational properties; see some treatment of this in [29,28,74,57,33]. In practice, it seems that implementations of CLP languages use f.p. computation although, evidently, any correct CLP compiler must use exact computation Ultimately, the CLP compiler must try to balance the opposing demands of correctness and efficiency: some mixed mode computational ability ....

J. Cox and K. McAloon. Decision Procedures for Constraint Based Extensions of Datalog, chapter 2. MIT-Press, 1993.

....the size of the database typically dominates by several orders of magnitude the size of the query. Datalog with integer (gap) order constraints programs and Datalog with constraints on set variables are evaluable in closed form on constraint databases with DEXPTIME complete data complexity [23, 11, 24]. Datalog 1S [7] an extension of Datalog with a successor function applied always to the first argument of relations, can be evaluated in closed form and has PSPACE complete data complexity. Datalog with periodicity constraints [26] relational calculus with linear repeating points [17] and ....

....Safe stratified Datalog : Z queries were not considered before in the literature. In [23] the data complexity of Datalog Z queries is shown to be in PTIME if the size of each constant in the database is logarithmic in the size of the entire database and to be in DEXPTIME in general. In [11] the expression complexity in general is shown to be DEXPTIME complete. In [24] the data complexity in general is also shown to be DEXPTIME complete. To proceed with the analysis of data complexity, we start with a definition of families of functions F i of type N N . Let F 0 be the set of ....

J. Cox, K. McAloon. Decision Procedures for Constraint Based Extensions of Datalog. In: Constraint Logic Programming, MIT Press, 1993.

....temporal constraint databases. This fact remains true even if we consider indefinite relational databases vs. indefinite temporal constraint databases. Unfortunately, the presence of indefinite information makes query evaluation intractable in many cases. Our analysis complements the results of [Rev90, CM93] and extends the results of [KKR90, vdM92] The research reported in [SRR] is closely related to our own. This paper investigates the use of constraints for the representation of infinite and indefinite information in a simple object oriented model. The authors do not consider the properties of an ....

J. Cox and K. McAloon. Decision Procedures for Constraint Based Extensions of Datalog. In F. Benhamou and A. Colmerauer, editors, Constraint Logic Programming: Selected Research. MIT Press, 1993. Originally appeared as Technical Report No. 90-09, Dept. of Computer and Information Sciences, Brooklyn College of C.U.N.Y.

.... temporal information [vdM92, Kou92, Kou93] If one surveys the existing work on databases with interpreted data and implicit representations, one finds contributions on the expressiveness of the various representation formalisms [Bau, BNW91, BCW93] on the complexity of query evaluation [Cho90, CM90, Rev90, vdM92], and on data structures and algorithms to be used in the representation of constraint expressions and in query evaluation [FVP92, Sri92, BJM93, BLL93, KRVV93] However, much less has been done on extending other parts of traditional database theory, for instance schema design and dependency ....

J. Cox and K. McAloon. Decision procedures for constraint based extensions of Datalog. Tech. Report 90-9, Dept. of Computer and Information Science, Brooklyn College of C.U.N.Y., Brooklyn, NY, 1990.

....constraint solvers which can exploit the geometric aspects of the problem to speed the computation. One may wish to give up the expressive power of PROLOG and restrict oneself to a language with bounded complexity. But even here, most natural CLP languages have at least DEXP time query complexity [7, 5]. We now classify the various geometric domains of interest. One dimension. In 1 dimension , we have subrings of C: integers, rationals, real algebraic numbers and general algebraic numbers. All these domains have associated exact computational methods. Already here, one can run into (single) ....

J. Cox and K. McAloon. Decision Procedures for Constraint Based Extensions of Datalog, chapter 2. MIT-Press, 1993.

....is compared in [146] 147] also combines modulus constraints with integer gap order constraints. Datalog with gap order constraints is shown to have a closed form and a DEXPTIMEcomplete data complexity in [121, 122] The expression complexity of the same language is shown to be in DEXPTIME in [47]. Recent work adds stratified negation to Datalog with gap order constraints with some syntactical safety restrictions. The resultant language has a non elementary data complexity [123] The relationship between syntactical safety as given in [123] and semantical safety is discussed in [136] and ....

J. Cox, K. McAloon. Decision Procedures for Constraint Based Extensions of Datalog. In: Constraint Logic Programming, MIT Press, 1993.

....2 Z and g 0. Revesz showed that Datalog Z queries over integer gap order databases can be evaluated bottom up in closed form. In addition recognizing whether a certain tuple is in the answer to a query can be done with PTIME data complexity. Independently this problem has also been solved in [CM93] CM93] have also considered gap order constraints over a dense domain and study combined complexity of query evaluation. The only difference with [Rev90] is that [CM93] consider combined complexity of query evaluation which is EXPTIME. The previous papers adopt a rather theoretical perspective. ....

....g 0. Revesz showed that Datalog Z queries over integer gap order databases can be evaluated bottom up in closed form. In addition recognizing whether a certain tuple is in the answer to a query can be done with PTIME data complexity. Independently this problem has also been solved in [CM93] CM93] have also considered gap order constraints over a dense domain and study combined complexity of query evaluation. The only difference with [Rev90] is that [CM93] consider combined complexity of query evaluation which is EXPTIME. The previous papers adopt a rather theoretical perspective. On a ....

[Article contains additional citation context not shown here]

J. Cox and K. McAloon. Decision Procedures for Constraint Based Extensions of Datalog. In F. Benhamou and A. Colmerauer, editors, Constraint Logic Programming: Selected Research. MIT Press, 1993. Originally appeared as Technical Report No. 90-09, Dept. of Computer and Information Sciences, Brooklyn College of C.U.N.Y.

....when we add recursion and negation to the existential fragment of relational calculus with diPCL (or dePCL) constraints [Rev90] has showed that Datalog with integer gaporder constraints (a subclass of diPCL constraints) can be evaluated bottom up in closed form with PTIME data complexity. CM90] showed that the combined complexity of the same problem is EXPTIME (and it remains the same if the domain is densely ordered) Rev90] has also proved that every Turing computable function can be expressed by a program in stratified Datalog : with integer order constraints. We would like to ....

J. Cox and K. McAloon. Decision Procedures for Constraint Based Extensions of Datalog. Technical Report 90-09, Dept. of Computer and Information Sciences, Brooklyn College of C.U.N.Y., 1990.

....of aggregate operators as is done recently in [8] However, even without the addition of aggregate operators constraint query languages can be quite expressive. Many types of non ground databases were used before in both constraint logic programming and constraint query languages in general (e.g. [2, 4, 9, 10, 11, 13, 15, 17, 23, 25, 26, 28, 30]) and with particular view to temporal database applications (e.g. 3, 6, 7, 16, 20, 21] However, constraint databases with set order constraints were not considered before. As the following example shows many interesting problems can be solved using set order constraints. Example 1.1 Consider ....

....Datalog ae P(Z) with the Datalog with integer order query language Datalog Z . In [25] the data complexity of Datalog Z queries is shown to be in PTIME if the size of each constant in the database is logarithmic in the size of the entire database and to be in DEXPTIME in general. In [10] the expression complexity in general is shown to be DEXPTIME complete. We show that the data complexity in general is also DEXPTIME complete. Theorem 5.1 There is a fixed yes no program Q in Datalog Z such that deciding whether Q(d) is yes for variable database d is DEXPTIME complete. ....

J. Cox, K. McAloon. Decision Procedures for Constraint Based Extensions of Datalog. In: Constraint Logic Programming, MIT Press, 1993.

....some half addition constraints are not gap order constraints. For example, x y 5 is a half addition constraint but it is not expressible by gap order constraints. A least fixpoint evaluation for Datalog with gap order constraints is described in [24] The recognition problem is also studied in [8]. The DISCO system [5] implements Datalog queries with integer gap order constraints. Adding negation in a safe way to Datalog with gap order queries is studied in [25] A temporal constraint is like a gap order constraint but the gap value can be any integer (both negative and non negative) ....

J. Cox, K. McAloon. Decision Procedures for Constraint Based Extensions of Datalog. In: F. Benhamou, A. Colmerauer, eds., Constraint Logic Programming, MIT Press, 1993.

.... for representing incomplete temporal information [31, 23] If one surveys the existing work on databases with interpreted data and implicit representations, one finds contributions on the expressiveness of the various representation formalisms [2, 5, 4] on the complexity of query evaluation [9, 12, 25, 31], and on data structures and algorithms to be used in the representation of constraint expressions and in query evaluation [28, 7, 8, 22] However, much less has been done on extending other parts of traditional database theory, for instance schema design and dependency theory. It should be clear ....

J. Cox and K. McAloon. Decision procedures for constraint based extensions of Datalog. In F. Benhamou and A. Colmerauer, editors, Constraint Logic Programming: Selected Research. MIT Press, 1993.

....over TCDB. This fact remains true even if we consider indefinite relational databases vs. ITCDB. The most important contribution of our work is the derivation of the upper bounds in the above tables; the lower bounds follow easily from published work. Our analysis complements the results of [42,10] and extends the results of [26,27,50] 42,43,10] have studied Datalog with integer gap order constraints (a subset of the atomic constraints allowed by diPCL) 26,27] have studied L constraint databases where L is the language of rational order with constants Complexity type Query language ....

....we consider indefinite relational databases vs. ITCDB. The most important contribution of our work is the derivation of the upper bounds in the above tables; the lower bounds follow easily from published work. Our analysis complements the results of [42,10] and extends the results of [26,27,50] [42,43,10] have studied Datalog with integer gap order constraints (a subset of the atomic constraints allowed by diPCL) 26,27] have studied L constraint databases where L is the language of rational order with constants Complexity type Query language RC TC 9 k RC TC Data complexity LOGSPACE ....

J. Cox and K. McAloon. Decision Procedures for Constraint Based Extensions of Datalog. In F. Benhamou and A. Colmerauer, editors, Constraint Logic Programming: Selected Research. MIT Press, 1993. Originally appeared as Technical Report No. 90-09, Dept. of Computer and Information Sciences, Brooklyn College of C.U.N.Y.

....a region for which this check succeeds, becomes a disjunct in the DNF form of OE 0 . Similar techniques have been used in [26] The technical tools which we will introduce immediately come from the temporal constraint literature [11] Similar tools have also been used under various names in [42,9] for studying the complexity of query evaluation for Datalog with integer gap order constraints. Let C be a set (i.e. conjunction) of dePCL or diPCL inequalities in variables x 1 ; x n . The binary inequality constraint network (BICN) associated with C is a labeled directed graph G = V; ....

J. Cox and K. McAloon. Decision Procedures for Constraint Based Extensions of Datalog. Technical Report 90-09, Dept. of Computer and Information Sciences, Brooklyn College of C.U.N.Y., 1990.

....magnitude the size of the query. Datalog with integer (gap) order constraints programs and Datalog with constraints on set variables are evaluable in closed form on constraint databases with Safe Query Languages for Constraint Databases Delta 3 DEXPTIME complete data complexity [Revesz 1993; Cox and McAloon 1993; Revesz 1995] Datalog 1S [Chomicki 19] an extension of Datalog with a successor function applied always to the first argument of relations, can be evaluated in closed form and has PSPACE complete data complexity. Datalog with periodicity constraints [Toman et al. 1994] relational calculus with ....

Cox, J. and McAloon, K. 1993. Decision Procedures for Constraint Based Extensions of Datalog. MIT Press.

....calculus over relational databases, to queries in relational calculus with temporal constraints over temporal constraint databases. This fact remains true even if we consider indefinite relational databases vs. indefinite temporal constraint databases. This analysis complements the results of [Rev90, CM93] and extends the results of [KKR90, vdM92] It also answers the questions posed in [Cho93] with respect to the model of [Kou93] The paper is organized as follows. The next section defines the abstract notions of constraints, constraint languages and constraint databases, and their concrete ....

....Proof: sketch) For the combined complexity case the upper bounds follow from Theorems 4.1 and 4.3. For the data complexity case the LOGSPACE bounds follow from [FR75] or modifications of the algorithms of [Kou94b] The lower bounds follows from [CH82] The above theorem complements the results of [Rev90, CM93] and extends the results of [KKR90] Rev90, CM93] have studied Datalog with integer gaporder constraints i.e. a subset of diPCL constraints. They have shown that evaluating queries in Datalog with integer gap order constraints can be done with PTIME data complexity [Rev90] and EXPTIME combined ....

[Article contains additional citation context not shown here]

J. Cox and K. McAloon. Decision Procedures for Constraint Based Extensions of Datalog. In F. Benhamou and A. Colmerauer, editors, Constraint Logic Programming: Selected Research. MIT Press, 1993. Originally appeared as Technical Report No. 90-09, Dept. of Computer and Information Sciences, Brooklyn College of C.U.N.Y.

....the DNF form of OE 0 . Similar techniques have been used in the context of query processing in constraint databases by [KKR90] The technical tools which we will introduce immediately come from the temporal constraint literature [DMP89] Similar tools have also been used under various names in [Rev90, CM90] for studying the complexity of query evaluation for Datalog with integer gap order constraints. Let C be a set (i.e. conjunction) of diPCL inequalities in variables x 1 ; xn . The binary inequality constraint network (BICN) associated with C is a labeled directed graph G = V; E) where ....

....Z, g 2 Z and g 0. Revesz showed that Datalog Z queries over integer gap order databases can be evaluated in closed form. In addition recognizing whether a certain tuple is in the answer to a query can be done with PTIME data complexity. 3 Independently the above problem has been solved in [CM90] who have also considered gap order constraints over a dense domain. The only difference with [Rev90] is that [CM90] do not consider data complexity thus the complexity of their query evaluation procedure is EXPTIME. 3 The notion of data complexity was originally introduced in [Var82] in the ....

[Article contains additional citation context not shown here]

J. Cox and K. McAloon. Decision Procedures for Constraint Based Extensions of Datalog. Technical Report 90-09, Dept. of Computer and Information Sciences, Brooklyn College of C.U.N.Y., 1990.

....temporal constraint databases. This fact remains true even if we consider indefinite relational databases vs. indefinite temporal constraint databases. Unfortunately, the presence of indefinite information makes query evaluation intractable in many cases. Our analysis complements the results of [Rev90, CM93] and extends the results of [KKR90, vdM92] Acknowledgements I would like to thank Timos Sellis for his support and encouragement. I would also like to thank Peter Revesz and Paris Kanellakis for promptly answering my questions concerning their work on constraint databases. ....

J. Cox and K. McAloon. Decision Procedures for Constraint Based Extensions of Datalog. In F. Benhamou and A. Colmerauer, editors, Constraint Logic Programming: Selected Research. MIT Press, 1993. Originally appeared as Technical Report No. 90-09, Dept. of Computer and Information Sciences, Brooklyn College of C.U.N.Y.

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J. Cox, K. McAloon. Decision Procedures for Constraint Based Extensions of Datalog. In: Constraint Logic Programming, MIT Press, 1993.

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