The expressiveness of a family of finite set languages

We precisely characterise the complexity of a set based database language called SRL, which presents a unified framework for queries and updates. By imposing simple syntactic restrictions on this language, we are able to capture exactly the classes, PTIME and LOGSPACE. We determine which additional operators would keep us in PTIME and show the surprising fact that the addition of Lists or a New operator increases the complexity of the language all the way to PRIMITIVE RECURSIVE. We also discuss the role of ordering in database query languages and show that the hom operator of the Machiavelli language in [OBB] does not capture all the order-independent polynomial-time properties.

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