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22
Towards Tractable Algebras for Bags
, 1993
"... Bags, i.e. sets with duplicates, are often used to implement relations in database systems. In this paper, we study the expressive power of algebras for manipulating bags. The algebra we present is a simple extension of the nested relation algebra. Our aim is to investigate how the use of bags in ..."
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Cited by 61 (4 self)
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Bags, i.e. sets with duplicates, are often used to implement relations in database systems. In this paper, we study the expressive power of algebras for manipulating bags. The algebra we present is a simple extension of the nested relation algebra. Our aim is to investigate how the use of bags in the language extends its expressive power, and increases its complexity. We consider two main issues, namely (i) the impact of the depth of bag nesting on the expressive power, and (ii) the complexity and the expressive power induced by the algebraic operations. We show that the bag algebra is more expressive than the nested relation algebra (at all levels of nesting), and that the difference may be subtle. We establish a hierarchy based on the structure of algebra expressions. This hierarchy is shown to be highly related to the properties of the powerset operator. Invited to a special issue of the Journal of Computer and System Sciences selected from ACM Princ. of Database Systems,...
On the expressive power of database queries with intermediate types
 Journal of Computer and System Sciences
, 1991
"... The setheight of a complex object type is defined to be its level of nesting of the set construct. In a query of the complex object calculus which maps a database D to an output type T,anintermediate type is a type which is used by some variable of the query, but which is not present in D or T.Fore ..."
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Cited by 44 (2 self)
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The setheight of a complex object type is defined to be its level of nesting of the set construct. In a query of the complex object calculus which maps a database D to an output type T,anintermediate type is a type which is used by some variable of the query, but which is not present in D or T.Foreachk, i ≥ 0 we define CALCk,i to be the family of calculus queries mapping from and to types with setheight ≤ k and using intermediate types with setheight ≤ i. In particular, CALC0,0 is the classical relational calculus, and CALC0,1 is equivalent to the family of secondorder (relational) queries. Several results concerning these families of languages are obtained. A primary focus is on the families CALC0,i, which map relations to relations. Upper and lower bounds in terms of hyperexponential time and space on the complexity of these families are provided. The CALC0,i hierarchy does not collapse with respect to expressive power. The union ∪0≤iCALC0,i is exactly the family of elementary queries, i.e., queries with hyperexponential complexity. The expressive power of queries from the complex object calculus interpreted using semantics based on the use of arbitrarily large finite or infinite set of invented values is studied. Under these semantics, the expressive power of the relational calculus is not increased, and the CALC0,i hierarchy collapses at CALC0,1. In general, queries with these semantics may not be computable. We also consider an alternative semantics which yields a family of queries equivalent to the computable queries. 1
A NestedGraph Model for the Representation and Manipulation of Complex Objects
 ACM Transactions on Information Systems
, 1994
"... this paper we report upon a graphbased approach to such an integration. Our use of graphs has two key advantages : firstly, graphs are formally defined, wellunderstood structures; secondly, it is widely accepted that graphbased formalisms considerably enhance the usability of complex systems [19] ..."
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Cited by 36 (4 self)
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this paper we report upon a graphbased approach to such an integration. Our use of graphs has two key advantages : firstly, graphs are formally defined, wellunderstood structures; secondly, it is widely accepted that graphbased formalisms considerably enhance the usability of complex systems [19]. Graphs have been used in conjunction with a number of conventional data models, for example the hierarchical and network models [35], the entityrelationship model [9] and a recent extension thereof for complex objects [27], and various semantic data models [16, 20, 31]. Graphs or hypergraphs [6] have also been used more recently in [12, 17, 23, 25, 33, 36] as a data modelling tool in their own right. We give a comparison between this recent work and our own approach in Section 4 of the paper. Directed graphs have also been the foundation of Hypertext databases [11, 33]. Such databases are graphs consisting of nodes which refer to units of stored information (typically text) and of named links. Each link connects two nodes, the "source" and the "destination". Links are traversed either forwards (from source to destination) or backwards (from destination to source). The process of traversing named links and examining the text associated with nodes is called
The Expressiveness of a Family of Finite Set Languages
 IN PROCEEDINGS OF 10TH ACM SYMPOSIUM ON PRINCIPLES OF DATABASE SYSTEMS
, 1991
"... In this paper we characterise exactly the complexity of a set based database language called SRL, which presents a unified framework for queries and updates. By imposing simple syntactic restrictions on it, we are able to express exactly the classes, P and LOGSPACE. We also discuss the role of orde ..."
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Cited by 26 (3 self)
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In this paper we characterise exactly the complexity of a set based database language called SRL, which presents a unified framework for queries and updates. By imposing simple syntactic restrictions on it, we are able to express exactly the classes, P and LOGSPACE. We also discuss the role of ordering in database query languages and show that the hom operator of Machiavelli language in [OBB89] does not capture all the orderindependent properties.
Tractable Query Languages for Complex Object Databases
, 1995
"... The expressiveness and complexity of several calculusbased query languages for complex objects is considered. Unlike previous investigations, we are concerned with the complexity of queries on databases of complex objects, rather than flat databases. This raises new issues specific to complex objec ..."
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Cited by 26 (4 self)
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The expressiveness and complexity of several calculusbased query languages for complex objects is considered. Unlike previous investigations, we are concerned with the complexity of queries on databases of complex objects, rather than flat databases. This raises new issues specific to complex objects. For instance, it is shown that the way the database makes use of its higherorder types has direct impact on query complexity. The use of fixpoint operators is shown to yield languages wellbehaved with respect to complexity and expressiveness. In particular, an extension of the fixpoint queries to complex objects is shown to express precisely the PTIME queries, under the assumption that the database makes "full" use of all its types. Similar results involve rangerestricted queries. 1 Introduction Complex objects are increasingly part of advanced database systems. They provide the structural core of objectoriented databases. Several query languages for complex objects have been propo...
Domain Independence and the Relational Calculus
 Acta Informatica
, 1993
"... Several alternative semantics (or interpretations) of the relational (domain) calculus are studied here. It is shown that they all have the same expressive power, i.e., the selection of any of the semantics neither gains nor loses expressive power. Since the domain is potentially infinite, the answe ..."
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Cited by 22 (7 self)
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Several alternative semantics (or interpretations) of the relational (domain) calculus are studied here. It is shown that they all have the same expressive power, i.e., the selection of any of the semantics neither gains nor loses expressive power. Since the domain is potentially infinite, the answer to a relational calculus query is sometimes infinite (and hence not a relation). The following approaches which guarantee the finiteness of answers to queries are studied here: outputrestricted unlimited interpretation, domain independent queries, outputrestricted finite and countable invention, and limited interpretation. Of particular interest is the outputrestricted unlimited interpretation  although the output is restricted to the active domain of the input and query, the quantified variables range over the infinite underlying domain. While this is close to the intuitive interpretation given to calculus formulas, the naive approach to evaluating queries under this semantics calls ...
On the Complexity of Queries in the Logical Data Model
 THEORETICAL COMPUTER SCIENCE
, 1993
"... We investigate the complexity of query processing in the logical data model (LDM). We use two measures: data complexity, which is complexity with respect to the size of the data, and expression complexity, which is complexity with respect to the size of the expressions denoting the queries. Our inve ..."
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Cited by 18 (0 self)
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We investigate the complexity of query processing in the logical data model (LDM). We use two measures: data complexity, which is complexity with respect to the size of the data, and expression complexity, which is complexity with respect to the size of the expressions denoting the queries. Our investigation shows that while the operations of product and union are essentially firstorder operations, the power set operation is inherently a higherorder operation and is exponentially expensive. We define a hierarchy of queries based on the depth of nesting of power set operations and show that this hierarchy corresponds to a natural hierarchy of Turing machines that run in multiply exponential time.
An Algebra for Pomsets
, 1995
"... We study languages for manipulating partially ordered structures with duplicates (e.g. trees, lists). As a general framework, we consider the pomset (partially ordered multiset) data type. We introduce an algebra for pomsets, which generalizes traditional algebras for (nested) sets, bags and list ..."
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Cited by 17 (3 self)
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We study languages for manipulating partially ordered structures with duplicates (e.g. trees, lists). As a general framework, we consider the pomset (partially ordered multiset) data type. We introduce an algebra for pomsets, which generalizes traditional algebras for (nested) sets, bags and lists. This paper is motivated by the study of the impact of different language primitives on the expressive power. We show that the use of partially ordered types increases the expressive power significantly. Surprisingly, it turns out that the algebra when restricted to both unordered (bags) and totally ordered (lists) intermediate types, yields the same expressive power as fixpoint logic with counting on relational databases. It therefore constitutes a rather robust class of relational queries. On the other hand, we obtain a characterization of PTIME queries on lists by considering only totally ordered types.
Complexity of Nonrecursive Logic Programs with Complex Values
 In Proceedings of the 17th ACM SIGACTSIGMODSIGART Symposium on Principles of Database Systems (PODS’98
, 1998
"... We investigate complexity of the SUCCESS problem for logic query languages with complex values: check whether a query defines a nonempty set. The SUCCESS problem for recursive query languages with complex values is undecidable, so we study the complexity of nonrecursive queries. By complex values we ..."
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Cited by 17 (2 self)
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We investigate complexity of the SUCCESS problem for logic query languages with complex values: check whether a query defines a nonempty set. The SUCCESS problem for recursive query languages with complex values is undecidable, so we study the complexity of nonrecursive queries. By complex values we understand values such as trees, finite sets, and multisets. Due to the wellknown correspondence between relational query languages and datalog, our results can be considered as results about relational query languages with complex values. The paper gives a complete complexity classification of the SUCCESS problem for nonrecursive logic programs over trees depending on the underlying signature, presence of negation, and range restrictedness. We also prove several results about finite sets and multisets. 1 Introduction A number of complexity results have been established for logic query languages. They are surveyed in [49, 18]. The major themes in these results are the complexity and expr...
A Query Language for ListBased Complex Objects
 In Thirteenth ACM SIGMOD Intern. Symposium on Principles of Database Systems (PODS'94
, 1994
"... We present a language for querying listbased complex objects. The language is shown to express precisely the polynomialtime generic listobject functions. The iteration mechanism of the language is based on a new approach wherein, in addition to the list over which the iteration is performed, a se ..."
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Cited by 15 (5 self)
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We present a language for querying listbased complex objects. The language is shown to express precisely the polynomialtime generic listobject functions. The iteration mechanism of the language is based on a new approach wherein, in addition to the list over which the iteration is performed, a second list is used to control the number of iteration steps. During the iteration, the intermediate results can be moved to the output list as well as reinserted into the list being iterated over. A simple syntactic constraint allows the growth rate of the intermediate results to be tightly controlled which, in turn, restricts the expressiveness of the language to PTIME. Data Parallel Systems Inc., 4617 Morningside Dr., Bloomington, IN, 47408; email: colby@dpsi.com y University of Regina, Dept. of Comp. Science, Regina, Saskatchewan S4S 0A2, Canada, email: saxton@cs.uregina.ca z Indiana University, Comp. Science Dept., Bloomington, IN 474054101, email: vgucht@cs.indiana.edu. 1 Intro...