On Computing Restricted Projections of Representative Instances

A lossless database scheme with a set of full implicational dependencies is considered. It is shown that the restricted projection of the representative instance onto the set of all the attributes is expressed by a first-order formula only if the following condition holds. The dependencies of the database scheme are equivalent to a set consisting of a single join dependency and several equality generating dependencies. If the database scheme has only tuple generating dependencies, then the condition states that these dependencies are equivalent to a join dependency, and in this case it is also a sufficient condition. If there are functional dependencies and a single join dependency and the database scheme is independent, then union of tableaux for restricted projections (and even for tableau queries) can be constructed in the worst case in exponential time and in some cases in polynomial time. A simpler characterization of independent database schemes is given.