The expressiveness of a family of finite set languages
PODS '91 Proceedings of the tenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
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The bounded-iteration construct foreach x in R|p(x) do t(x) is very commonly used in database programming, due to the fact that database programs are dominated by data retrieval and manipulation tasks rather than complex computations. Hence in database programming language design, it is important to understand the expressive power of the bounded-iteration construct and its relationship with other language constructs. We study the bounded-iteration construct within the context of a simple database programming language called the iterative transaction language. The language is shown to have NPTIME expressive power, and the deterministic subclass of it has PTIME expressive power. We show that the bounded-iteration construct is essential for achieving polynomial-time expressiveness, by characterizing its relationship with other constructs in the language. We also identify a natural subclass of iterative transactions called first-order transactions with exactly first-order expressive power. The complexity of first-order transactions in terms of iteration depth and intermediate states is connected further to the complexity of first-order updates in terms of quantification depth.