Expressiveness of Efficient Semi-Deterministic Choice Constructs

Recently, Abiteboul and Kanellakis introduced the notion of determinate query to describe database queries having the ability to create new domain elements. As there are no natural determinate-complete query languages known, more restrictive (the constructive queries) and more general (the semi-deterministic queries) notions of query were considered. Here, we show that the advantage of the second approach over the rst is not so much in increased expressiveness, but in the ability of expressing queries more eeciently. Concretely, we provide a precise characterization of a minimal subclass of the semi-deterministic queries containing the constructive queries in which the polynomial-time counting queries can be expressed eeciently. This subclass is deened via a semi-deterministic query language, which is obtained by introducing a particular choice operation, called swap-choice. The main claim of this paper is further substantiated by showing that the introduction of swap-choice, when restricted to new domain elements, is polynomial-time equivalent to the introduction of counting. This equivalence sheds new light on the signiicance of polynomial-time counting queries: in particular , it shows that, in the absence of an explicit domain ordering, a very limited amount of non-determinism suuces to express this important class of queries ef-ciently.