# An Algebra for Pomsets

@inproceedings{Grumbach1995AnAF, title={An Algebra for Pomsets}, author={St{\'e}phane Grumbach and Tova Milo}, booktitle={Inf. Comput.}, year={1995} }

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) datatype. 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…

## 43 Citations

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## References

SHOWING 1-10 OF 49 REFERENCES

### Towards tractable algebras for bags

- Mathematics, Computer SciencePODS '93
- 1993

It is shown that the bag algebra is more expressive than the nested relation algebra (at all levels of nesting), and that the difference may be subtle, and a hierarchy is established based on the structure of algebra expressions.

### New techniques for studying set languages, bag languages and aggregate functions

- Computer SciencePODS '94
- 1994

The bounded degree property which says that the number of distinct in- and out-degrees in the output of a graph query does not depend on the size of the input if the input is “simple” is studied.

### Structural Recursion as a Query Language

- Computer ScienceDBPL
- 1991

A programming paradigm that tries to get close to both the semantic simplicity of relational algebra, and the expressive power of unrestricted programming languages, and it is expected that lower-level programming, and therefore better optimization will be feasible.

### Logical and Computational Aspects of Programming with Sets/Bags/Lists

- Computer ScienceICALP
- 1991

Back-and-forth translations between the two presentations of the list, bag, and set datatypes are established, from which it follows that they are equally expressive, and results relating proofs of program properties, in the two presentation are established.

### The complexity of relational query languages (Extended Abstract)

- Computer ScienceSTOC '82
- 1982

The pattern which will be shown is that the expression complexity of the investigated languages is one exponential higher then their data complexity, and for both types of complexity the authors show completeness in some complexity class.

### Ordered Types in the AQUA Data Model

- Computer Science, MathematicsDBPL
- 1993

A query algebra that supports ordering among the data elements and its associated data model with special emphasis on ordered types and their operators is presented.

### Calculi for Bags and their Complexity

- Computer Science, MathematicsDBPL
- 1993

This paper provides here two restricted calculi with bounded complexity, and shows that the restrictions are minimal, indeed, any looser restriction leads to non computable queries.

### Untyped sets, invention, and computable queries

- Computer SciencePODS '89
- 1989

Conventional database query languages are considered in the context of untyped sets and the calculus has power beyond the computable queries; and is characterized using the typed complex object calculus with invention.

### Tractable query languages for complex object databases

- Computer SciencePODS '91
- 1991

The expressiveness and complexity of several calculus-based query languages for complex objects are considered and an extension of the fixpoint queries to complex objects is shown to express precisely the PTIME queries, under the assumption that the database makes full use of all its types.