Adequacy of decompositions of relational databases
Journal of computer and system sciences (Print)
We consider conditions that have appeared in the literature with the purpose of defining a "good" decomposition of a relation scheme. We show that these notions are equivalent in the case that all constraints in the database are functional dependencies. This result solves an open problem of Rissanen. However, for arbitrary constraints the notions are shown to differ. I. BASIC DEFINITIONS We assume the reader is familiar with the relational model of data as expounded by Codd [ 111, in which data
... are represented by tables called relations. Rows of the tables are tuples, and the columns are named by attributes. The notation used in this paper is that found in Ullman  . A frequent viewpoint is that the "real world" is modeled by a universal set of attributes R and constraints on the set of relations that can be the "current" relation for scheme R (see Beeri et al.  , Aho et al. [ 11, and Beeri et al. ). The database scheme representing the real world is a collection of (nondisjoint) subsets of the * RELATIONAL DATABASES 369 univesal relation scheme R; each of these subsets is called a relation scheme. The database is an assignment of relations (sets of tuples) to the relation schemes. The database desigri problem is to pick a database scheme p = (R, ,..., Rk) with (Jf= i R, = R, such that, informally: (1) The "current" relation for R, which does not really exist in the database, can be discovered from the "current" values of the Rts, which do exist in the database. (2) The constraints on the legal relations for scheme R can be enforced by constraints on the relations for the Rts. (3) The Rl's have certain desirable properties, usually connected with the constraints, such as lack of redundancy.