S. Grumbach and V. Vianu. Tractable query languages for complex object databases. In Proc. 10th ACM Symp. on Principles of Database Systems, pages 315--327, Boulder, May 1991.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....orders, and (2) understanding the expressive power of constants and equality. In terms of comparison of this paper s contribution with related work in descriptive computational complexity: a) Higher order logic has been used to express various exponential time and space classes, e.g. see [25, 22, 15, 26]. However, the exact characterizations given in this paper are more economical in basic primitives. b) There are similarities between the approaches of [21, 20] and [27] Both approaches add primitives to the TLC to encode P. The principal difference is that TLC = equality and constants ....

S. Grumbach and V. Vianu. Tractable Query Languages for Complex Object Databases. In Proceedings of the 10th ACM Symposium on the Principles of Database Systems, pp. 315--327. ACM Press, 1991.

....transitive closure and parity are not expressible in the polynomialspace fragment of the powerset al..gebra for nested relations. 1 This fragment consists of all powerset al..gebra expressions where all intermediate results are of polynomial size, on each database. We also mention Grumbach and Vianu [GV95], who also studied a sparsity notion in connection with queries over nested relational databases, although they considered sparsity as a property of databases rather than of query language expressions. Suciu and Paredaens conjectured in general that the polynomial space fragment of the powerset ....

S. Grumbach and V. Vianu. Tractable query languages for complex object databases. Journal of Computer and System Sciences, 51(2):149-- 167, 1995.

....5 Expressive power In this section, we compare the expressive power of the languages CALC cv , CALC cv , CALC cv , Datalog cv , COL and their em allowed versions. We then focus on bounding complexity of queries by limiting the ranges of variables in evaluating the query. As in [9], we consider using fix point operators to provide tractable recursion, and limiting the arity and height of higher order types. The complex value query languages described in the Appendix without external functions are equivalent [10] This result also hold for the query languages extended with ....

....can be evaluated by using polynomial space in the size of their arguments, then sem (CALC cv ) QPSPACE. A database is dense with respect to a type T if it makes full use of the type T . An i; k type is a type whose set height is at most i and whose tuple width is at most k. As in [9], we consider density with respect to the set of i; k types, rather than individual types. Consider an i; k database schema R and let I inst(R) Then I is dense with respect to i; k types if there exists a polynomial P such that, for each I 2 I , jdom( i; k ;atom(I) j P(jIj) See ....

[Article contains additional citation context not shown here]

S. Grumbach and V. Vianu. Tractable Query Languages for Complex Object Databases. In Journal of Computer and System Sciences, 51(2):149-167, 1995.

.... of languages, based on restrictions on the types of intermediate results and show that the calculus can express all elementary time (or space) queries [35, 45] Exact complexity characterizations are obtained with fixpoint, which is no longer redundant when the level of set nesting is bounded [30]. The algebra proposed in the earlier models did not incorporate powerset and could not express this operation. It turns out that when considering mappings from relations to relations, the algebra without powerset does not provide more expressive power than relational algebra (or calculus) so ....

....with powerset , is too powerful. This emphasizes the significance of our result that the strictly safe calculus is equivalent to the algebra without powerset . Additionally, some restrictions on the calculus guaranteeing ptime bound and closely related to our strict safety, are exhibited in [30]. We study also here a rule based language. In the rule based paradigm, nesting can be expressed in many ways. Indeed, a main difference between various proposals of logic programming with a set construct is in their approach to nesting: grouping in LDL [15] data functions in COL [3] and a form ....

, S. Grumbach and V. Vianu, Tractable Query Languages for Complex Object Databases, Proc. ACM PODS, 1991.

....and in [19] a bound for the result of the fixpoint operator is precomputed. Both approaches give us precisely the PTIME queries over nested sets when a total order on the domain of atomic elements is available (this follows from the results in the papers cited above and in [13] It is shown in [10] that tractability may be obtained, in the context of complex object languages, by a combination of restrictions and assumptions about the input database. They considered families of calculi with restrictions on set nesting and showed that if the input database is dense 1 with respect to its ....

....and languages with aggregation in the presence of fixpoint operators. In [17] it is shown that BQL has the same expressive power as the nested relational language with aggregate functions over the natural numbers, denoted by NRL nat . It is known how to capture PTIME over the nested relations [10, 13, 19], and it is also known how to capture many complexity classes for arithmetic functions [4, 15] Thus, one might ask if the correspondence between BQL and NRL nat allows us to enrich the latter to capture PTIME in both worlds: relational and arithmetical. We shall prove a few initial results ....

S. Grumbach and V. Vianu. Tractable query languages for complex object databases. J. Comput. and Syst. Sci. 51(2): 149--167, 1995.

....and constraint databases as systems of objects. The present survey will cover logic program constraint databases, which were first articulated as such in [KKR90, KKR95] The reader is referred to [BSCE97, Bro96, GS95] for information on object oriented constraint databases, and also to [GS95, GV91, RKS88] for some information on complex constraint objects and their precursors in the nested relational models. Classical relational databases and classical logic programs have always been closely related, because the tuples of a relation are equivalent to the ground facts of a logic program. A ....

S. Grumbach and V. Vianu. Tractable query language for complex object databases. In Proceedings of PODS Symposium, pages 315--326, 1991.

....model theory (cf. Section 13) 1 General Introduction Computability over sets (of tuples of sets of tuples of sets, etc. or over complex objects is at present rather popular subject, especially in connection with nested data bases. There may be distinguished two directions: typed (e.g. [1, 13, 19, 22]) and untyped (cf. 6, 7, 8, 26, 30, 32, 34] ones. The first is based on the direct product and powerset type constructs and presupposes, at least at the beginning, the hyperexponential (i.e. Kalmar elementary) computational complexity. Some additional special efforts are necessary to find ....

....product and powerset type constructs and presupposes, at least at the beginning, the hyperexponential (i.e. Kalmar elementary) computational complexity. Some additional special efforts are necessary to find restrictions (on the types height, ranges of variables, density sparsity of data wrt types [13]) giving rise to more tractable query languages. The second direction is not concerned with exponentiation because it is based on the notion HF of Hereditarily Finite Both authors from Program Systems Institute of Russian Acad. of Sci. Pereslavl Zalessky, 152140, Russia. e mail: ....

Grumbach, S., Vianu, V.: Tractable query languages for complex object databases. Rapports de Recherche N1573. INRIA. 1991

....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] ....

Grumbach S. and Vianu V. [1995], `Tractable query languages for complex object databases', Journal of Computer and System Sciences 51(2), 149--167.

....and prove that its range restricted fragment is equivalent to NRA with bounded fixpoints. Keywords: nested relational algebra, conservative extension, complex objects, fixpoints, indexes. 1 Introduction Several query languages for databases with complex objects have been studied in recent years [AGVW89, AK89, AB88, BNTW95, dB92, GV91, GF88, GG91, GG92, HS89, HS91, PG92]. A natural way of designing such a language is to extend first order logic to a logic for hereditary finite sets, and consider only domainindependent queries, like in the case of first order logic. Abiteboul and Beeri follow this path in [AB88] define safe queries, and show that the resulting ....

....has been recently proven that the restricted fixpoint has the same expressive power as the bounded fixpoint [GSG95] In consequence all properties for the bounded fixpoints reported in this paper carry over to the restricted fixpoints. Second, Grumbach and Vianu discuss range restricted CALC IFP [GV91], which relies on a carefully designed set of range restriction rules for the fixpoint. Its relationship to the bounded fixpoints is open. As a step towards a comparison, we present in Section 6 a range restricted, logic based calculus with fixpoints which we show to be equivalent to NRA bfix : ....

[Article contains additional citation context not shown here]

Stephane Grumbach and Victor Vianu. Tractable query languages for complex object databases. In Proceedings of 10th ACM Symposium on Principles of Database Systems, 1991.

....1 Introduction CPL is a language for updating complex value databases. Because of the deep nesting involved in such databases, representing updates in a concise way and optimizable spezification is an intriguing problem. While query languages for complex value databases have been well studied [2, 35, 5, 17], the issue of updating such databases has not. For example, a standard for object oriented query languages is given in [10] OQL) but there is no mention of updates apart from the notion of a transaction. Updates in object oriented databases are most often performed through methods, which are ....

Stephane Grumbach and Victor Vianu. Tractable query languages for complex object databases. Technical Report 1573, INRIA, Rocquencourt BP 105, 78153 Le Chesnay, France, December 1991. Extended abstract appeared in PODS 91.

....i.e. lists of tuples of lists. In contrast, our result shows that all PTIME queries can be expressed even when only flat lists are available. 7 Nesting We next consider ordered types with nesting. Nesting of structures has been extensively studied in the context of unordered types like sets [HS88, HS89, GV90, GV91] and bags [GM93] In this section, we study the combined effect of order, nesting, and duplicates. Nested pomsets can be used to represent ordered types with components of some ordered type (e.g. lists of trees) In nested pomsets, every object can be a nested pomset or a tuple with attributes ....

....PALG 1 . We next consider PALG 2 , one stage higher in the nesting hierarchy. We study the relationship between the nested pomset al..gebra and the nested relation and nested bag algebras. We denote the nested relation (bag) algebra when restricted to set nesting of depth k, RALG k (BALG k ) [HS88, GV91, GM93]. We first compare RALG 2 , BALG 2 and PALG 2 restricted to queries over (nested) sets. Theorem 7.1 RALG 2 ae BALG 2 ae PALG 2 . The strict inclusion of RALG 2 in BALG 2 was proved in [GM93] It was also shown there that BALG 2 is included in PSPACE. The strict inclusion BALG ....

S. Grumbach and V. Vianu. Tractable query languages for complex object databases. In Proc. 10th ACM Symp. on Principles of Database Systems, pages 315--327, Boulder, May 1991.

.... investigated collection type is that of complex objects (see [Hul87, ABGG89, AK89] and the references therein) Variations on the theme are nested relations [JS82] and V relations [SAB 87, AB86] Algebras and or logical calculi (with or without fixpoints) are presented in [KV84, AB88, RKS88, GV91, KV93] as well as in [TF86, SS86, Col90] where they are called nested relational algebras. BBW92] offers a rational reconstruction of the nested relational algebras (NRA) starting from the monad constructs as well as connections between s.r. and the algebra with powerset of [AB88] That NRA at ....

Stephane Grumbach and Victor Vianu. Tractable query languages for complex object databases. Technical Report 1573, INRIA, Rocquencourt BP 105, 78153 Le Chesnay, France, December 1991. Extended abstract appeared in PODS 91.

....We also define a complex object logic based language with fixpoints and prove that its range restricted fragment is equivalent to NRA with bounded fixpoints. 1 Introduction Several query languages for databases with complex objects have been studied in recent years (e.g. 1] 2] 3] 9] [12], 13] 14] 17] 20] 22] A natural way of designing such a language is to extend first order logic to a logic for hereditary finite sets, and consider only domain independent queries, like in the case of first order logic. Abiteboul and Beeri follow this path in [1] define safe queries, ....

....Abiteboul and Vianu prove in [7] that the inflationary and partial fixpoint have the same expressive power over first order logic iff PTime = PSpace, which most people believe to be false. We also present a logic based language having the same expressive power as NRA bfix. Grumbach and Vianu in [12] also present a tractable logic based language which can express recursive queries, but we do not know its precise expressive power, or whether it is closed under map (as our language is) We hope to be able to clarify in the future the relationship between our language and that presented in [12] ....

[Article contains additional citation context not shown here]

S. Grumbach, V. Vianu, Tractable Query Languages for Complex Object Databases, Proc ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, 1991

....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. Grumbach and V. Vianu. Tractable query languages for complex object databases. Journal of Computer and System Sciences, 51(2):149-- 167, 1995.

....updates, expressed as conventional CPL expressions, into equivalent update expressions in CPL . As a result of applying these transformations, the performance of complex updates can increase substantially. 1 Introduction Although query languages for complex value databases have been well studied [3, 35, 6, 18], the issue of updating such databases has not. For example, a standard for object oriented query languages is given in [11] OQL) but there is no mention of updates apart from the notion of a transaction. Update languages for any model are, however, clearly important since databases are ....

Stephane Grumbach and Victor Vianu. Tractable query languages for complex object databases. Technical Report 1573, INRIA, Rocquencourt BP 105, 78153 Le Chesnay, France, December 1991. Extended abstract appeared in PODS 91.

....a rm computable Sigma query, where is a set type ( f 0 g) Then f can be expressed in NRA( Sigma [ n) fix, over the class C. Proof The proof consists just in a simulation, in the language NRA( Sigma[n) fix, of some relational machine RM. This is done with classical techniques, see [21, 15]. No encoding decoding of the input is necessary. During the simulation, the values of the r registers are kept as a value of type oe 1 Theta : Theta oe r . The final result is easily extracted, because is a set type. 2 5 Computable Sigma Queries Can Be Computed by Relational Machines In ....

....symbols are present in Sigma (i.e. k = 0) then it suffices to pick any n integers to encode x 1 ; xn , say 0; 1; n Gamma 1, because the mapping 0 (x i ) i Gamma 1, with 0 undefined elsewhere, is a partial isomorphism. This fact is essential in proofs like those in [21, 15], where Turing machines are simulated within database query languages. But when Sigma 6= OE, the above 0 is no longer a partial isomorphism. The idea is to search systematically for k functions with finite domains c1 ; ck , and a finite partial isomorphism 0 : A; p A 1 ; ....

S. Grumbach, V. Vianu, Tractable Query Languages for Complex Object Databases, Proc ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, 1991

.... and logic programming have been considered in (Abiteboul Grumbach 1988, Abiteboul Grumbach 1991, Kuper 1990, Beeri, Naqvi, Schmueli Tsur 1991, Vadaparty 1991, Shmueli, Tsur Zaniolo 1992, Leone Rullo 1993, Beeri Kornatzky 1994, Abiteboul Beeri 1995, Kanella kis, Kuper Revesz 1995, Grumbach Vianu 1995, Dovier, Omodeo, Pontelli Rossi 1996, Dantsin Voronkov 1997a, Voronkov 1992, Voronkov 1997) In this paper we extend unification, the core mechanism of logic programming, to handling bags and sets. This extension implies changes in the standard logic programming semantics, namely the ....

Grumbach, S. & Vianu, V. (1995), `Tractable query languages for complex object databases', Journal of Computer and System Sciences 51(2), 149--167.

....The second direction follows from the fact that every Pom Alg operation increases at most exponentially the size of its input. 7 Nesting We next consider ordered types with nesting. Nesting of structures has been extensively studied in the context of unordered types like sets [HS88, HS89, GV90, GV91] and bags [GM93] In this section, we study the combined effect of order, nesting, and duplicates. Nested pomsets can be used to represent ordered types with components of some ordered type (e.g. lists of trees) In nested pomsets, every object can be a nested pomset or a tuple with attributes ....

..... We next consider Pom Alg , one stage higher in the nesting hierarchy. We study the relationship between the nested pomset al..gebra and the nested relation and nested bag algebras. We denote the nested relation (bag) algebra when restricted to set nesting of depth k, RALG (BALG ) HS88, GV91, GM93] We first compare RALG BALG and Pom Alg restricted to queries over (nested) sets. ae Pom Alg . The strict inclusion of RALG in BALG was proved in [GM93] It was also shown there that BALG is included in PSPACE. The strict inclusion BALG in Pom Alg follows ....

S. Grumbach and V. Vianu. Tractable query languages for complex object databases. In Proc. 10th ACM Symp. on Principles of Database Systems, pages 315--327, Boulder, May 1991.

....second direction follows from the fact that every Pom Alg operation increases at most exponentially the size of its input. 2 7 Nesting We next consider ordered types with nesting. Nesting of structures has been extensively studied in the context of unordered types like sets [HS88, HS89, GV90, GV91] and bags [GM93] In this section, we study the combined effect of order, nesting, and duplicates. Nested pomsets can be used to represent ordered types with components of some ordered type (e.g. lists of trees) In nested pomsets, every object can be a nested pomset or a tuple with attributes ....

....We next consider Pom Alg 2 , one stage higher in the nesting hierarchy. We study the relationship between the nested pomset al..gebra and the nested relation and nested bag algebras. We denote the nested relation (bag) algebra when restricted to set nesting of depth k, RALG k (BALG k ) HS88, GV91, GM93] We first compare RALG 2 , BALG 2 and Pom Alg 2 restricted to queries over (nested) sets. Theorem 7.1 RALG 2 ae BALG 2 ae Pom Alg 2 . The strict inclusion of RALG 2 in BALG 2 was proved in [GM93] It was also shown there that BALG 2 is included in PSPACE. The strict ....

S. Grumbach and V. Vianu. Tractable query languages for complex object databases. In Proc. 10th ACM Symp. on Principles of Database Systems, pages 315--327, Boulder, May 1991.

....n children is labeled ff, then its children are labeled ff:1; ff:n. Instances are labeled similarly, with the children of a set node labeled ff, all labeled ff:0. So an instance and its type have the same set of labels. Instances can sometimes underuse their type. It has been shown in [GV95] that it has a strong impact on the expressive power of query languages. In the present context, we show that it is fundamental for finding the schema. An instance underuses its type for example when set types are used to model objects that always have the same cardinality (and would have been ....

S. Grumbach and V. Vianu. Tractable query languages for complex object databases. Journal of Computer and System Sciences, 51(2):149--167, 1995.

....safe queries wrt a complexity class in a given language. We next consider a syntactic criterion called range restriction, defined in 4 Without loss of generality, we assume in the following that no variable symbol occurs both free and bound, or is bound by more than one quantifier. GV91b] and show that it provides sufficient conditions for safety wrt PTIME and PSPACE, for CALC and its fixpoint extensions. We shall see that, under certain assumptions, rangerestricted queries express all safe queries wrt PTIME and PSPACE. We first define inductively range restricted formulas in ....

S. Grumbach and V. Vianu. Tractable query languages for complex object databases. In Proc. 10th ACM Symp. on Principles of Database Systems, Boulder, May 1991.

....second direction follows from the fact that every Pom Alg operation increases at most exponentially the size of its input. 2 7 Nesting We next consider ordered types with nesting. Nesting of structures has been extensively studied in the context of unordered types like sets [HS88, HS89, GV90, GV91] and bags [GM93] In this section, we study the combined effect of order, nesting, and duplicates. Nested pomsets can be used to represent ordered types with components of some ordered type (e.g. lists of trees) In nested pomsets, every object can be a nested pomset or a tuple with attributes ....

....We next consider Pom Alg 2 , one stage higher in the nesting hierarchy. We study the relationship between the nested pomset al..gebra and the nested relation and nested bag algebras. We denote the nested relation (bag) algebra when restricted to set nesting of depth k, RALG k (BALG k ) HS88, GV91, GM93] We first compare RALG 2 , BALG 2 and Pom Alg 2 restricted to queries over (nested) sets. Theorem 7.1 RALG 2 ae BALG 2 ae Pom Alg 2 . The strict inclusion of RALG 2 in BALG 2 was proved in [GM93] It was also shown there that BALG 2 is included in PSPACE. The strict ....

S. Grumbach and V. Vianu. Tractable query languages for complex object databases. In Proc. 10th ACM Symp. on Principles of Database Systems, pages 315--327, Boulder, May 1991.

....in FO . On the other hand, a great amount of research has been done on hierarchical database structures, in particular, those constructed using the tuple and set constructs such as the nested or non first normal form relations (e.g. JS82, FT83, RKS88] and the complex objects (e.g. [AB87, HS91, GV91]) Query languages for complex objects have been extensively studied, and their complexity is now well understood. Complex objects provide a modeling power which is fundamental in the context of constraint databases. In flat query languages for constraint databases, the universe is restricted to ....

....sets by the tuple and set constructs. A logic based query language C CALC is also proposed which uses the active domain semantics. In particular, the language allows quantifying over sets. We study the complexity and expressive power of the new language and show that essentially the results [HS91, GV91] for query languages of classical complex objects carry over to the context of constraint databases. For example, when restricted to flat input and output, C CALC expresses exactly all constraint queries having hyper exponential time (space) complexity; the hierarchy based on setheight does not ....

[Article contains additional citation context not shown here]

S. Grumbach and V. Vianu. Tractable query languages for complex object databases. In Proc. ACM Symp. on Principles of Database Systems, pages 315--327, 1991.

....queries can be evaluated in polynomial time. The earliest proposal to introduce complex values appears to be [Mak77] Equivalent complex value calculus and algebra are proposed in [KV84, KV93, AB95] Tractable restrictions are considered by many authors, including [JS82, TF86, RKS86, AB95, PG88, GV91] Extended notions of completeness. Classical relational queries return answers built from the elements of dom present in the input. In contrast, queries in objectoriented databases often return structures that contain newly constructed objects. These are represented by new identifiers (values ....

S. Grumbach and V. Vianu, Tractable query languages for complex object databases, Proc. ACM Symp. on Principles of Database Systems, 1991.

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