# Repetitions and permutations of columns in the semijoin algebra

Dirk Leinders; Jan Van Den Bussche

RAIRO - Theoretical Informatics and Applications (2008)

- Volume: 43, Issue: 2, page 179-187
- ISSN: 0988-3754

## Access Full Article

top## Abstract

top## How to cite

topLeinders, Dirk, and Van Den Bussche, Jan. "Repetitions and permutations of columns in the semijoin algebra." RAIRO - Theoretical Informatics and Applications 43.2 (2008): 179-187. <http://eudml.org/doc/92910>.

@article{Leinders2008,

abstract = {
Codd defined the relational algebra [E.F. Codd, Communications of the ACM13 (1970) 377–387;
E.F. Codd, Relational completeness of data base sublanguages, in Data Base Systems, R. Rustin, Ed.,
Prentice-Hall (1972) 65–98] as the
algebra with operations projection, join, restriction, union and
difference. His projection operator can drop, permute and repeat
columns of a relation. This permuting and repeating of columns does
not really add expressive power to the relational algebra. Indeed,
using the join operation, one can rewrite any relational algebra
expression into an equivalent expression where no projection
operator permutes or repeats columns. The fragment of the relational
algebra known as the semijoin algebra, however, lacks a full join
operation. Nevertheless, we show that any semijoin algebra
expression can still be simulated in a natural way by a set of
expressions where no projection operator permutes or repeats
columns.
},

author = {Leinders, Dirk, Van Den Bussche, Jan},

journal = {RAIRO - Theoretical Informatics and Applications},

keywords = {Database; relational algebra; semijoin algebra; projection.; database; projection},

language = {eng},

month = {6},

number = {2},

pages = {179-187},

publisher = {EDP Sciences},

title = {Repetitions and permutations of columns in the semijoin algebra},

url = {http://eudml.org/doc/92910},

volume = {43},

year = {2008},

}

TY - JOUR

AU - Leinders, Dirk

AU - Van Den Bussche, Jan

TI - Repetitions and permutations of columns in the semijoin algebra

JO - RAIRO - Theoretical Informatics and Applications

DA - 2008/6//

PB - EDP Sciences

VL - 43

IS - 2

SP - 179

EP - 187

AB -
Codd defined the relational algebra [E.F. Codd, Communications of the ACM13 (1970) 377–387;
E.F. Codd, Relational completeness of data base sublanguages, in Data Base Systems, R. Rustin, Ed.,
Prentice-Hall (1972) 65–98] as the
algebra with operations projection, join, restriction, union and
difference. His projection operator can drop, permute and repeat
columns of a relation. This permuting and repeating of columns does
not really add expressive power to the relational algebra. Indeed,
using the join operation, one can rewrite any relational algebra
expression into an equivalent expression where no projection
operator permutes or repeats columns. The fragment of the relational
algebra known as the semijoin algebra, however, lacks a full join
operation. Nevertheless, we show that any semijoin algebra
expression can still be simulated in a natural way by a set of
expressions where no projection operator permutes or repeats
columns.

LA - eng

KW - Database; relational algebra; semijoin algebra; projection.; database; projection

UR - http://eudml.org/doc/92910

ER -

## References

top- S. Abiteboul, R. Hull and V. Vianu, Foundations of Databases. Addison-Wesley (1995). Zbl0848.68031
- H. Andréka, I. Németi and J. van Benthem, Modal languages and bounded fragments of predicate logic. J. Philosophical Logic27 (1998) 217–274. Zbl0919.03013
- E.F. Codd, A relational model of data for large shared data banks. Communications of the ACM13 (1970) 377–387. Zbl0207.18003
- E.F. Codd, Relational completeness of data base sublanguages, in Data Base Systems, R. Rustin, Ed. Prentice-Hall (1972) pp. 65–98.
- E. Grädel, On the restraining power of guards. J. Symbolic Logic64 (1999) 1719–1742. Zbl0958.03027
- E. Grädel, Guarded fixed point logics and the monadic theory of countable trees. Theor. Comput. Sci.288 (2002) 129–152. Zbl1061.03022
- E. Grädel, C. Hirsch and M. Otto, Back and forth between guarded and modal logics. ACM Transactions on Computational Logic3 (2002) 418–463.
- E. Grädel and I. Walukiewicz, Guarded fixed point logic, in Proceedings of the 14th IEEE Symposium on Logic in Computer Science LICS '99 (1999) pp. 45–54.
- D. Leinders and J. Van den Bussche, On the complexity of division and set joins in the relational algebra. J. Comput. Syst. Sci.73 (2007) 538–549. Special issue with selected papers on database theory. Zbl1115.68066
- D. Leinders, M. Marx, J. Tyszkiewicz and J. Van den Bussche, The semijoin algebra and the guarded fragment. J. Logic, Language and Information14 (2005) 331–343. Zbl1080.03012
- D. Leinders, J. Tyszkiewicz and J. Van den Bussche, On the expressive power of semijoin queries. Inform. Process. Lett.91 (2004) 93–98. Zbl1178.68202