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,...

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.

The Collection Programming Language (CPL) is based on a complex value model of data, and has successfully been used for querying, transforming and integrating data from a wide variety of structured data sources -- relational, ACeDB, and ASN.1 among others. However, since there is no notion of objects and classes in CPL, it cannot adequately model recursive types or inheritance, and hence cannot be used to query object-oriented databases (OODBs). By adding a reference type and four operations to CPL -- dereference, method invocation, identity test and class type cast -- it is possible to express a large class of interesting "safe" queries against OODBs. As an example of how the extended CPL can be used to query an OODB, we will describe how the extended language has been used as a query interface to Shore databases. 1 Introduction A vast amount of data currently exists in databases, files formatted according to various data exchange formats, and application programs. Although much of t...

Sets and bags are closely related structures. A bag is different from a set in that it is sensitive to the number of times an element occurs while a set is not. In this paper, we introduce the concept of web bag in a web warehouse as a part of our Web Information Coupling System(WICS). Informally, a web bag is a web table which allows multiple occurrences of identical web tuples. Web bag helps to discover useful knowledge from a web table such as visible documents (or web sites), luminous documents and luminous paths. We formally discuss the semantics and properties of web bags, and illustrate with examples applications of web bag in knowledge discovery in a web warehouse. 1 Introduction Sets and bags are closely related structures. When a set is allowed to have multiple occurrences of a member, it is called a bag or multi-set [29]. While a set of tuples (i.e., a relation) is a simple, natural model of data as it might appear in a database, commercial systems are rarely if ever bas...

Most database theory focused on investigating databases containing sets of tuples. In practice databases often implement relations using bags, i.e. sets with duplicates. In this paper we study how database query languages are affected by the use of duplicates. We consider query languages that are simple extensions of the (nested) relational algebra, and investigate their resulting expressive power and complexity. 1 Introduction In the standard approach to database modeling, relations are assumed to be sets, and no duplicates are allowed. For real applications, many systems relax this restriction [Fis87, HM81] and support bags in their data model, often to save the cost of duplicate elimination. Efforts have been made for providing a theoretical framework for such systems. Algebras for manipulating bags were developed by extending the relational algebra [Alb91, Klu82, OOM87], and optimization techniques for these algebras were studied [BK90, Mum90, Alb91]. Computational aspects of...

Most database theory focused on investigating databases containing sets of tuples. In practice databases often implement relations using bags, i.e. sets with duplicates. In this paper we study how database query languages are affected by the use of duplicates. We consider query languages that are simple extensions of the (nested) relational algebra, and investigate their resulting expressive power and complexity. 1 Introduction In the standard approach to database modeling, relations are assumed to be sets, and no duplicates are allowed. For real applications, many systems relax this restriction [Fis87, HM81] and support bags in their data model, often to save the cost of duplicate elimination. Efforts have been made for providing a theoretical framework for such systems. Algebras for manipulating bags were developed by extending the relational algebra [Alb91, Klu82, OOM87], and optimization techniques for these algebras were studied [BK90, Mum90, Alb91]. Computational aspects of...