Abstract
There is a well-known algorithm for determining when a decomposition of a database relation scheme has a lossless join with respect to a set of functional dependencies. We first present a reformulation of this algorithm in terms of set closures. For the special case of m=2, there is a well-known explicit condition for losslessness. Our formulation extends this result for general m. Also, our formulation leads to a strong necessary condition for ρ to be lossless. Separately, we prove a sufficient condition for ρ to be lossless. Finally, we present a sufficient condition, and a necessary condition for ρ to be lossless with respect to a set of functional and multivalued dependencies.
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