Equivalence of views by query capacity

Tim Connors
1985 Proceedings of the fourth ACM SIGACT-SIGMOD symposium on Principles of database systems - PODS '85  
The ability of view users to retrieve information contained in a database is studied. A measure of this ability, called "query capacity," is introduced and shown to be valuable for defining important concepts concerning views. Three such notions, namely equivalence, redundancy, and decomposition of views, are identified and investigated. A key tool, called "template substitution," is introduced to aid in these investigations. Among the major results obtained are the following: (1)
more » ... ons of view equivalence and redundancy in views. (2) The decidabihty of view equivalence. (3) A technique to eliminate redundancy in views. (4) The decomposition of a view into an essentially unique normal form. fi '. 1986 Academic Press. Inc. During the past decade, database management systems have been an increasingly important tool for the design, implementation, and application of information systems. The successful use of a database management system requires the selection of (i) a structure for information within the database (referred to here as a database schema) and (ii) a description of the specific data appropriate to each user (referred to here as a view) [6, 19, 201. A major impediment to this selection process is the absence of an adequate method for measuring the respective capabilities of competing views and database schemata. Several such measurement methods for database schemata have been proposed [ 1, 5, 16) . However, these measurement methods are inappropriate for views due to the special relationship between a view and its underlying database schema. The purpose of this paper is to introduce an appropriate measure of the capability of views and to study relationships between views of identical capability. Ultimately, the capability of a view is determined by the set of all view queries. For this reason, our measure of the capability of a view is based on the collective ability of the view queries to retrieve information contained in the underlying database. It is shown that each view query has a "surrogate" database query which always produces the same result. The set of all such "surrogates" is called the "query capacity" of a view and formally represents the capability of a view. The EQUIVALENCEOFVIEWSBYQUERYCAPACITY 235 notion of query capacity provides a simple means for defining and studying many concepts and questions pertaining to the query capability of user views. In particular, the equivalence of, redundancy in, and normal forms for views are all easily and naturally expressable using query capacity. These conepts are formally defined and explored in the paper. The above three concepts are investigated in the context of the relational model of data. Two invaluable tools used in these investigations are the well-known template representation for queries [2] and a new template operation called "template substitution," Using this operation, a template-based description is obtained of the query capacity of a view. The theory of templates is then used extensively to prove many of our results. Among these are the decidability of view equivalence, a characterization of redundancy in views, and the existence of a unique normal form for views based on "decompositions," The paper is divided into four sections. The first reviews the relational model of data and introduces the elementary notions of "query capacity" and "view equivalence." Several results are presented to motivate and display the naturalness of these notions. In addition, an important characterization of view equivalence in terms of "query set closure" is established. In the second section, the notion of template is reviewed and "template substitution" introduced. A powerful constructive formulation of "query set closure" is then presented and used to establish several results about decidability. The third section is devoted to the study of redundancy in views. It is shown that each view has an equivalent "nonredundant" view. Also, the "nonredundant" views equivalent to a given view are shown to be bounded in size, a result which yields insight into the relationship between "closed query sets" and "query capacity" of a view. In addition, many results are presented about the interaction between the (non)redundancy of a view and template representations of the queries defining the view. The fourth section introduces and examines "simplified" views, a normal form for views. It is shown that every view has an equivalent simplified view. In addition, several results about the relationship between a view and a simplified equivalent are established. These facts are then used to show the uniqueness of simplified views equivalent to a given view. Finally, a result is presented which testifies to the naturalness of simplified views as a normal form. I. FUNDAMENTALS In this section we review, and slightly extend, the known basic concepts needed for the development of our results. In addition, we introduce the notions of query capacity and view equivalence. We present several results which underscore the naturalness of these notions and warrant their study in the remainder of the paper. This study commences in the present section with two important characterization theorems. The first characterizes query capacity in terms of special sets of queries 571133/2-8
doi:10.1145/325405.325422 dblp:conf/pods/Connors85 fatcat:cb23hg6qafcqbhmxsjc7kheazm