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Some Analytic Tools for the Design of Relational Database Systems

Making use of arguments from information theory it is shown that a boolean function can represent multivalued dependencies. A method is described by which a hypergraph can be constructed to represent dependencies in a relation. A new normal form called generalized Boyce-Codd normal form is defined. An explicit formula is derived for representing dependencies that would remain in a projection of a relation. A definition of join is given which makes the derivation of many theoretical results easy. Another definition given is that of information in a relation. The information gets conserved whenever lossless decompositions are involved. It is shown that the use of null elements is important in handling data.