On the Power of Aggregation in Relational Query Languages

It is a folk result that relational algebra or calculus extended with aggregate functions cannot compute the transitive closure. However, proving folk results is sometimes a nontrivial task. In this paper, we tell the story of the work on expressive power of relational languages with aggregate functions. We also prove by far the most powerful result that describes the expressiveness of such languages. There are four main features of our result that distinguish it from previous ones: 1. It does not rely on any unproven assumptions, such as separation of complexity classes. 2. It establishes a general property of queries definable with the help of aggregate functions. This property can easily be applied to prove many expressiveness bounds. 3. The class of aggregate functions is much larger than any previously considered. 4. The proof is “non-syntactic.” That is, it does not depend on a specific syntax chosen for the language with aggregates.

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