# 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

### 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.

### Computing Possible and Certain Answers over Order-Incomplete Data

- Computer Science, MathematicsTheor. Comput. Sci.
- 2019

### Structural Recursion on Ordered Trees and List-Based Complex Objects

- Computer ScienceICDT
- 2007

This paper shows that the combination of vertical recursion down a tree combined with horizontal recursion across a list of trees gives rise to a robust class of transformations: it captures the class of all primitive recursive queries.

### Querying Order-Incomplete Data

- Computer Science
- 2014

This work extends the pos- itive relational algebra to ordered and order-incomplete data, and introduces a set of axioms to guide the design of a bag semantics for the language, and proposes concrete semantics satisfying the desiderata.

### Structural Recursion as a Query Language on Lists and Ordered Trees

- Computer ScienceTheory of Computing Systems
- 2008

It is shown that the combination of vertical recursion down a tree combined with horizontal recursion across a list of trees gives rise to a robust class of transformations: it captures the class of all primitive recursive queries.

### Tractable Iteration Mechanisms for Bag Languages

- Mathematics, Computer ScienceICDT
- 1997

It is shown that the deflationary and bounded inflationary fixpoint constructs are equally expressive and strictly more expressive than their set-based counterparts and that the bag algebra with bounded fixpoint fails to capture all PTIME queries over databases with ordered domains.

### Possible and Certain Answers for Queries over Order-Incomplete Data

- Computer Science, MathematicsTIME
- 2017

A query language for order-incomplete data, based on the positive relational algebra with order-aware accumulation, is introduced, which shows that these problems are respectively NP-complete and coNP-complete, but identifies many tractable cases depending on the query operators or input partial orders.

### Tractable Iteration Mechanisms forBag

- Mathematics
- 2009

The goal of this paper is to study tractable iteration mechanisms for bags. The presence of duplicates in bags prevents iteration mechanisms developed in the context of sets to be directly applied to…

### Leveraging the structure of uncertain data

- Computer Science
- 2016

This thesis investigates conditions on probabilistic relational instances that ensure the tractability of query evaluation and lineage computation and shows intractability under mild assumptions for any other condition on instances.

### Semantics analysis through elementary meanings: theoretical foundation for generalized thesaurus construction

- Computer Science
- 2000

This paper establishes the computational properties of Transducer Datalog, a query language based on a new machine model called a generalized sequence transducer, and develops a hierarchy of time-complexity classes based on the Ackermann function.

## 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.