An Algebra for Pomsets

Abstract

We study languages for manipulatingpartially orderedstructures withduplicates(e.g., trees, lists). As a general framework, we consider thepomset(partially ordered multiset) data type. We introduce an algebra forpomsets, which generalizes traditional algebras for (nested) sets, bags, and lists. This paper is motivated by the study of the impact of different language primitives on the expressive power. We show that the use of partially ordered types increases the expressive power significantly. Surprisingly, it turns out that the algebra when restricted to both unordered (bags) and totally ordered (lists) intermediate types, yields the same expressive power as fixpoint logic with counting on relational databases. It therefore constitutes a rather robust class of relational queries. On the other hand, we obtain a characterization of PTIME queries on lists by considering only totally ordered types.