Database states and their tableaux

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Abstract
Recent work considers a database state to satisfy a set of dependencies if there exists a satisfying universal relation whose projections contain each of the relations in the state. Such relations are called weak instances for the state. We propose the set of all weak instances for a state as an embodiment of the information represented by the state. We characterize states that have the same set of weak instances by the equivalence of their associated tableaux. We apply this notion to the comparison of database schemes and characterize all pairs of schemes such that for every legal state of one of them there exists an equivalent legal state of the other one. We use this approach to provide a new characterization of Boyce-Codd Normal Form relation schemes.

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