TY - JOUR
T1 - An Algebra for Pomsets
AU - Grumbach, Stéphane
AU - Milo, Tova
N1 - Funding Information:
* Work supported in part by the Esprit Project BRA FIDE 2. Work was done while the second author was visiting University of Toronto and supported by the Institute for Robotics and Intelligent Systems. An extended abstract appeared in the Proceedings of the 5th International Conference on Database Theory, Prague, 1995.
PY - 1999/5/1
Y1 - 1999/5/1
N2 - We study languages for manipulating partially ordered structures with duplicates (e.g., trees, lists). As a general framework, we consider the pomset (partially ordered multiset) data type. We introduce an algebra for pomsets, 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.
AB - We study languages for manipulating partially ordered structures with duplicates (e.g., trees, lists). As a general framework, we consider the pomset (partially ordered multiset) data type. We introduce an algebra for pomsets, 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.
UR - https://www.scopus.com/pages/publications/0347565242
U2 - 10.1006/inco.1998.2777
DO - 10.1006/inco.1998.2777
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AN - SCOPUS:0347565242
SN - 0890-5401
VL - 150
SP - 268
EP - 306
JO - Information and Computation
JF - Information and Computation
IS - 2
ER -