Optimization of Nested SQL

We present a new optimization method for nested SQL query blocks with aggregation operators. The method is derived from the theory of dependency implication. It uniies and generalizes previously proposed (seemingly unrelated) algorithms, and can incorporate general database dependencies given in the database schema. We apply our method to query blocks with max, min aggregation operators. We obtain an algorithm which does not infer arithmetical constraints, and reduces optimization of such query blocks to the well-studied problem of tableau equivalence. We prove a completeness result for this algorithm: if two max, min blocks can be merged, the algorithm will detect this fact.