On the composition and decomposition of attributes and tuples
In this paper NEST (UNNEST) is decomposed into attribute composition and tuple composition (into attribute decomposition and tuple decomposition, resp.). It is shown that by the complete graph and the edge labelling associated to a relation as in  we can represent the set of multi-valued dependencies in the given relation. Therefore, by this complete graph and edge labelling, we can represent Boolean dependencies and multivalued dependencies of the relation that we obtain from the given relation through tuple compositions and attribute compositions. A concept of insistency of operators is proposed. A necessary and sufficient condition for an operator to be ℱ-insistent for a given Boolean dependency ℱ is offered.
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