We investigate the problem of rewriting queries with aggregate operators using views that may or may not contain aggregate operators. A rewriting of a query is a second query that uses view predicates such that evaluating rst the views and then the rewriting yields the same result as evaluating the original query. In this sense, the original query and the rewriting are equivalent modulo the view de nitions. The queries and views we consider correspond to unnested SQL queries, possibly with union, that employ the operators min, max, count, and sum. Our approach is based on syntactic characterizations of the equivalence of aggregate queries. One contribution of this paper are characterizations of the equivalence of disjunctive aggregate queries, which generalize our previous results for the conjunctive case. For each operator , we introduce several types of queries using views as candidates for rewritings. We unfold such a candidate by replacing each occurrence of a view predicate with its de nition, thus obtaining a regular aggregate query. The candidates have a di erent, usually more complex operator than . We prove that unfolding the candidate, however, results in a regular aggregate query that is equivalent to the candidate modulo the view de nitions. This property justi es considering these types of queries as natural candidates for rewritings. In this way, we reduce the problem of whether there exist rewritings of a particular type to a problem involving equivalence. We distinguish between partial rewritings that contain at least one view predicate and complete rewritings that contain only view predicates. In contrast to previous work on this topic, we not only give su cient, but also necessary conditions for a rewriting to exist. More precisely, we show for each type of candidate that the existence of both, partial and complete rewritings is decidable, and we provide upper and lower complexity bounds.
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